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Exam: CBSE Class 12
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Q151
#151
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
Integrate
x
+
2
x
2
+
2
x
+
3
\frac{x+2}{\sqrt{x^2+2x+3}}
x
2
+
2
x
+
3
x
+
2
.
Show model answer
[QEx 7.4 Q21 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q152
#152
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
Integrate
x
+
3
x
2
−
2
x
−
5
\frac{x+3}{x^2-2x-5}
x
2
−
2
x
−
5
x
+
3
.
Show model answer
[QEx 7.4 Q22 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q153
#153
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
Integrate
5
x
+
3
x
2
+
4
x
+
10
\frac{5x+3}{\sqrt{x^2+4x+10}}
x
2
+
4
x
+
10
5
x
+
3
.
Show model answer
[QEx 7.4 Q23 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q154
#154
Mathematics → Integrals → Integrals of Some Particular Functions
·
Moderate
Add
∫
d
x
x
2
+
2
x
+
2
\int \frac{dx}{x^2+2x+2}
∫
x
2
+
2
x
+
2
d
x
equals
A
x
tan
−
1
(
x
+
1
)
+
C
x\tan^{-1}(x+1) + C
x
tan
−
1
(
x
+
1
)
+
C
B
tan
−
1
(
x
+
1
)
+
C
\tan^{-1}(x+1) + C
tan
−
1
(
x
+
1
)
+
C
C
(
x
+
1
)
tan
−
1
x
+
C
(x+1)\tan^{-1}x + C
(
x
+
1
)
tan
−
1
x
+
C
D
tan
−
1
x
+
C
\tan^{-1}x + C
tan
−
1
x
+
C
Tap an option to check your answer.
[QEx 7.4 Q24 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q155
#155
Mathematics → Integrals → Integrals of Some Particular Functions
·
Hard
Add
∫
d
x
9
x
−
4
x
2
\int \frac{dx}{\sqrt{9x-4x^2}}
∫
9
x
−
4
x
2
d
x
equals
A
1
9
sin
−
1
(
9
x
−
8
8
)
+
C
\frac{1}{9}\sin^{-1}\left(\frac{9x-8}{8}\right) + C
9
1
sin
−
1
(
8
9
x
−
8
)
+
C
B
1
2
sin
−
1
(
8
x
−
9
9
)
+
C
\frac{1}{2}\sin^{-1}\left(\frac{8x-9}{9}\right) + C
2
1
sin
−
1
(
9
8
x
−
9
)
+
C
C
1
3
sin
−
1
(
9
x
−
8
8
)
+
C
\frac{1}{3}\sin^{-1}\left(\frac{9x-8}{8}\right) + C
3
1
sin
−
1
(
8
9
x
−
8
)
+
C
D
1
2
sin
−
1
(
9
x
−
8
9
)
+
C
\frac{1}{2}\sin^{-1}\left(\frac{9x-8}{9}\right) + C
2
1
sin
−
1
(
9
9
x
−
8
)
+
C
Tap an option to check your answer.
[QEx 7.4 Q25 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q156
#156
Mathematics → Integrals → Integration by Partial Fractions
·
Moderate
Add
Find
∫
d
x
(
x
+
1
)
(
x
+
2
)
\int \frac{dx}{(x+1)(x+2)}
∫
(
x
+
1
)
(
x
+
2
)
d
x
.
Show model answer
[Q7.5 Eg.11 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q157
#157
Mathematics → Integrals → Integration by Partial Fractions
·
Moderate
Add
Find
∫
x
2
+
1
x
2
−
5
x
+
6
d
x
\int \frac{x^2+1}{x^2-5x+6}\,dx
∫
x
2
−
5
x
+
6
x
2
+
1
d
x
.
Show model answer
[Q7.5 Eg.12 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q158
#158
Mathematics → Integrals → Integration by Partial Fractions
·
Hard
Add
Find
∫
3
x
−
2
(
x
+
1
)
2
(
x
+
3
)
d
x
\int \frac{3x-2}{(x+1)^2(x+3)}\,dx
∫
(
x
+
1
)
2
(
x
+
3
)
3
x
−
2
d
x
.
Show model answer
[Q7.5 Eg.13 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q159
#159
Mathematics → Integrals → Integration by Partial Fractions
·
Hard
Add
Find
∫
x
2
(
x
2
+
1
)
(
x
2
+
4
)
d
x
\int \frac{x^2}{(x^2+1)(x^2+4)}\,dx
∫
(
x
2
+
1
)
(
x
2
+
4
)
x
2
d
x
.
Show model answer
[Q7.5 Eg.14 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q160
#160
Mathematics → Integrals → Integration by Partial Fractions
·
Hard
Add
Find
∫
(
3
sin
ϕ
−
2
)
cos
ϕ
5
−
cos
2
ϕ
−
4
sin
ϕ
d
ϕ
\int \frac{(3\sin\phi-2)\cos\phi}{5-\cos^2\phi-4\sin\phi}\,d\phi
∫
5
−
c
o
s
2
ϕ
−
4
s
i
n
ϕ
(
3
s
i
n
ϕ
−
2
)
c
o
s
ϕ
d
ϕ
.
Show model answer
[Q7.5 Eg.15 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q161
#161
Mathematics → Integrals → Integration by Partial Fractions
·
Hard
Add
Find
∫
x
2
+
x
+
1
(
x
+
2
)
(
x
2
+
1
)
d
x
\int \frac{x^2+x+1}{(x+2)(x^2+1)}\,dx
∫
(
x
+
2
)
(
x
2
+
1
)
x
2
+
x
+
1
d
x
.
Show model answer
[Q7.5 Eg.16 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q162
#162
Mathematics → Integrals → Integration by Partial Fractions
·
Easy
Add
Integrate the rational function
x
(
x
+
1
)
(
x
+
2
)
\frac{x}{(x+1)(x+2)}
(
x
+
1
)
(
x
+
2
)
x
.
Show model answer
[QEx 7.5 Q1 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q163
#163
Mathematics → Integrals → Integration by Partial Fractions
·
Easy
Add
Integrate the rational function
1
x
2
−
9
\frac{1}{x^2-9}
x
2
−
9
1
.
Show model answer
[QEx 7.5 Q2 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q164
#164
Mathematics → Integrals → Integration by Partial Fractions
·
Moderate
Add
Integrate the rational function
3
x
−
1
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
\frac{3x-1}{(x-1)(x-2)(x-3)}
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
3
x
−
1
.
Show model answer
[QEx 7.5 Q3 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q165
#165
Mathematics → Integrals → Integration by Partial Fractions
·
Moderate
Add
Integrate the rational function
x
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
\frac{x}{(x-1)(x-2)(x-3)}
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
x
.
Show model answer
[QEx 7.5 Q4 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q166
#166
Mathematics → Integrals → Integration by Partial Fractions
·
Easy
Add
Integrate the rational function
2
x
x
2
+
3
x
+
2
\frac{2x}{x^2+3x+2}
x
2
+
3
x
+
2
2
x
.
Show model answer
[QEx 7.5 Q5 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q167
#167
Mathematics → Integrals → Integration by Partial Fractions
·
Moderate
Add
Integrate the rational function
1
−
x
2
x
(
1
−
2
x
)
\frac{1-x^2}{x(1-2x)}
x
(
1
−
2
x
)
1
−
x
2
.
Show model answer
[QEx 7.5 Q6 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q168
#168
Mathematics → Integrals → Integration by Partial Fractions
·
Moderate
Add
Integrate the rational function
x
(
x
2
+
1
)
(
x
−
1
)
\frac{x}{(x^2+1)(x-1)}
(
x
2
+
1
)
(
x
−
1
)
x
.
Show model answer
[QEx 7.5 Q7 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q169
#169
Mathematics → Integrals → Integration by Partial Fractions
·
Moderate
Add
Integrate the rational function
x
(
x
−
1
)
2
(
x
+
2
)
\frac{x}{(x-1)^2(x+2)}
(
x
−
1
)
2
(
x
+
2
)
x
.
Show model answer
[QEx 7.5 Q8 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q170
#170
Mathematics → Integrals → Integration by Partial Fractions
·
Hard
Add
Integrate the rational function
3
x
+
5
x
3
−
x
2
−
x
+
1
\frac{3x+5}{x^3-x^2-x+1}
x
3
−
x
2
−
x
+
1
3
x
+
5
.
Show model answer
[QEx 7.5 Q9 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q171
#171
Mathematics → Integrals → Integration by Partial Fractions
·
Hard
Add
Integrate the rational function
2
x
−
3
(
x
2
−
1
)
(
2
x
+
3
)
\frac{2x-3}{(x^2-1)(2x+3)}
(
x
2
−
1
)
(
2
x
+
3
)
2
x
−
3
.
Show model answer
[QEx 7.5 Q10 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
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Q172
#172
Mathematics → Integrals → Integration by Partial Fractions
·
Moderate
Add
Integrate the rational function
5
x
(
x
+
1
)
(
x
2
−
4
)
\frac{5x}{(x+1)(x^2-4)}
(
x
+
1
)
(
x
2
−
4
)
5
x
.
Show model answer
[QEx 7.5 Q11 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q173
#173
Mathematics → Integrals → Integration by Partial Fractions
·
Moderate
Add
Integrate the rational function
x
3
+
x
+
1
x
2
−
1
\frac{x^3+x+1}{x^2-1}
x
2
−
1
x
3
+
x
+
1
.
Show model answer
[QEx 7.5 Q12 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q174
#174
Mathematics → Integrals → Integration by Partial Fractions
·
Moderate
Add
Integrate the rational function
2
(
1
−
x
)
(
1
+
x
2
)
\frac{2}{(1-x)(1+x^2)}
(
1
−
x
)
(
1
+
x
2
)
2
.
Show model answer
[QEx 7.5 Q13 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
Q175
#175
Mathematics → Integrals → Integration by Partial Fractions
·
Easy
Add
Integrate the rational function
3
x
−
1
(
x
+
2
)
2
\frac{3x-1}{(x+2)^2}
(
x
+
2
)
2
3
x
−
1
.
Show model answer
[QEx 7.5 Q14 · NCERT (CBSE Class 12) — Integrals (Chapter 7, NCERT Mathematics Part 2)]
Report
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