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Exam: Maharashtra HSC Class 12
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Set · 5 questions
Integrate the following functions w. r. t. x :
Q126
#126
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
(
x
+
1
)
2
x
2
+
3
d
x
\int (x + 1)\sqrt{2x^2 + 3}\, dx
∫
(
x
+
1
)
2
x
2
+
3
d
x
Show model answer
[QEx 3.3 II (viii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q127
#127
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
x
5
−
4
x
−
x
2
d
x
\int x \sqrt{5 - 4x - x^2}\, dx
∫
x
5
−
4
x
−
x
2
d
x
Show model answer
[QEx 3.3 II (ix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q128
#128
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
sec
2
x
⋅
tan
2
x
+
tan
x
−
7
d
x
\int \sec^2 x \cdot \sqrt{\tan^2 x + \tan x - 7}\, dx
∫
sec
2
x
⋅
tan
2
x
+
tan
x
−
7
d
x
Show model answer
[QEx 3.3 II (x) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q129
#129
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
2
+
2
x
+
5
d
x
\int \sqrt{x^2 + 2x + 5}\, dx
∫
x
2
+
2
x
+
5
d
x
Show model answer
[QEx 3.3 II (xi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q130
#130
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
2
x
2
+
3
x
+
4
d
x
\int \sqrt{2x^2 + 3x + 4}\, dx
∫
2
x
2
+
3
x
+
4
d
x
Show model answer
[QEx 3.3 II (xii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Set · 9 questions
Integrate the following functions w. r. t. x :
Q131
#131
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
(
2
+
cot
x
−
cosec
2
x
)
⋅
e
x
d
x
\int (2 + \cot x - \operatorname{cosec}^2 x) \cdot e^x\, dx
∫
(
2
+
cot
x
−
cosec
2
x
)
⋅
e
x
d
x
Show model answer
[QEx 3.3 III (i) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q132
#132
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
(
1
+
sin
x
1
+
cos
x
)
⋅
e
x
d
x
\int \left(\frac{1 + \sin x}{1 + \cos x}\right) \cdot e^x\, dx
∫
(
1
+
c
o
s
x
1
+
s
i
n
x
)
⋅
e
x
d
x
Show model answer
[QEx 3.3 III (ii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q133
#133
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
e
x
⋅
(
1
x
−
1
x
2
)
d
x
\int e^x \cdot \left(\frac{1}{x} - \frac{1}{x^2}\right)\, dx
∫
e
x
⋅
(
x
1
−
x
2
1
)
d
x
Show model answer
[QEx 3.3 III (iii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q134
#134
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
(
x
(
x
+
1
)
2
)
⋅
e
x
d
x
\int \left(\frac{x}{(x + 1)^2}\right) \cdot e^x\, dx
∫
(
(
x
+
1
)
2
x
)
⋅
e
x
d
x
Show model answer
[QEx 3.3 III (iv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q135
#135
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
e
x
x
[
x
(
log
x
)
2
+
2
(
log
x
)
]
d
x
\int \frac{e^x}{x} \left[x (\log x)^2 + 2 (\log x)\right]\, dx
∫
x
e
x
[
x
(
lo
g
x
)
2
+
2
(
lo
g
x
)
]
d
x
Show model answer
[QEx 3.3 III (v) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q136
#136
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
e
5
x
⋅
(
5
x
⋅
log
x
+
1
x
)
d
x
\int e^{5x} \cdot \left(\frac{5x \cdot \log x + 1}{x}\right)\, dx
∫
e
5
x
⋅
(
x
5
x
⋅
l
o
g
x
+
1
)
d
x
Show model answer
[QEx 3.3 III (vi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q137
#137
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
e
sin
−
1
x
⋅
(
x
+
1
−
x
2
1
−
x
2
)
d
x
\int e^{\sin^{-1} x} \cdot \left(\frac{x + \sqrt{1 - x^2}}{\sqrt{1 - x^2}}\right)\, dx
∫
e
s
i
n
−
1
x
⋅
(
1
−
x
2
x
+
1
−
x
2
)
d
x
Show model answer
[QEx 3.3 III (vii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q138
#138
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
log
(
1
+
x
)
(
1
+
x
)
d
x
\int \log (1 + x)^{(1 + x)}\, dx
∫
lo
g
(
1
+
x
)
(
1
+
x
)
d
x
Show model answer
[QEx 3.3 III (viii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q139
#139
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
cosec
(
log
x
)
[
1
−
cot
(
log
x
)
]
d
x
\int \operatorname{cosec} (\log x) \left[1 - \cot (\log x)\right]\, dx
∫
cosec
(
lo
g
x
)
[
1
−
cot
(
lo
g
x
)
]
d
x
Show model answer
[QEx 3.3 III (ix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Set · 11 questions
Integrate the following w. r. t. x :
Q140
#140
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
x
2
+
2
(
x
−
1
)
(
x
+
2
)
(
x
+
3
)
d
x
\int \frac{x^2 + 2}{(x - 1)(x + 2)(x + 3)} \, dx
∫
(
x
−
1
)
(
x
+
2
)
(
x
+
3
)
x
2
+
2
d
x
Show model answer
[QEx 3.4 I (i) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q141
#141
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
x
2
(
x
2
+
1
)
(
x
2
−
2
)
(
x
2
+
3
)
d
x
\int \frac{x^2}{(x^2 + 1)(x^2 - 2)(x^2 + 3)} \, dx
∫
(
x
2
+
1
)
(
x
2
−
2
)
(
x
2
+
3
)
x
2
d
x
Show model answer
[QEx 3.4 I (ii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q142
#142
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
12
x
+
3
6
x
2
+
13
x
−
63
d
x
\int \frac{12x + 3}{6x^2 + 13x - 63} \, dx
∫
6
x
2
+
13
x
−
63
12
x
+
3
d
x
Show model answer
[QEx 3.4 I (iii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q143
#143
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
2
x
4
−
3
x
−
x
2
d
x
\int \frac{2x}{4 - 3x - x^2} \, dx
∫
4
−
3
x
−
x
2
2
x
d
x
Show model answer
[QEx 3.4 I (iv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q144
#144
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
x
2
+
x
−
1
x
2
+
x
−
6
d
x
\int \frac{x^2 + x - 1}{x^2 + x - 6} \, dx
∫
x
2
+
x
−
6
x
2
+
x
−
1
d
x
Show model answer
[QEx 3.4 I (v) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q145
#145
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
6
x
3
+
5
x
2
−
7
3
x
2
−
2
x
−
1
d
x
\int \frac{6x^3 + 5x^2 - 7}{3x^2 - 2x - 1} \, dx
∫
3
x
2
−
2
x
−
1
6
x
3
+
5
x
2
−
7
d
x
Show model answer
[QEx 3.4 I (vi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q146
#146
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
12
x
2
−
2
x
−
9
(
4
x
2
−
1
)
(
x
+
3
)
d
x
\int \frac{12x^2 - 2x - 9}{(4x^2 - 1)(x + 3)} \, dx
∫
(
4
x
2
−
1
)
(
x
+
3
)
12
x
2
−
2
x
−
9
d
x
Show model answer
[QEx 3.4 I (vii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q147
#147
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Hard
Add
∫
1
x
(
x
5
+
1
)
d
x
\int \frac{1}{x(x^5 + 1)} \, dx
∫
x
(
x
5
+
1
)
1
d
x
Show model answer
[QEx 3.4 I (viii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q148
#148
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
2
x
2
−
1
x
4
+
9
x
2
+
20
d
x
\int \frac{2x^2 - 1}{x^4 + 9x^2 + 20} \, dx
∫
x
4
+
9
x
2
+
20
2
x
2
−
1
d
x
Show model answer
[QEx 3.4 I (ix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q149
#149
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
x
2
+
3
(
x
2
−
1
)
(
x
2
−
2
)
d
x
\int \frac{x^2 + 3}{(x^2 - 1)(x^2 - 2)} \, dx
∫
(
x
2
−
1
)
(
x
2
−
2
)
x
2
+
3
d
x
Show model answer
[QEx 3.4 I (x) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q150
#150
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
2
x
(
2
+
x
2
)
(
3
+
x
2
)
d
x
\int \frac{2x}{(2 + x^2)(3 + x^2)} \, dx
∫
(
2
+
x
2
)
(
3
+
x
2
)
2
x
d
x
Show model answer
[QEx 3.4 I (xi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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