PYQs Homework Notes Mocks Board Daily Homework MHT-CET Maths Question type Integral of e^x [f(x) + f'(x)] where f is a rational function This type of question, asked 7 times: 2 May 2023 S1, 3 May 2023 S1, 9 May 2023 S1, 13 May 2024 S2, 14 May 2024 S2, 20 Apr 2025 S2, 25 Apr 2025 S1. All 7 questions below, oldest first.
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Question 1 2 May 2023 S1
116 ∫ x + 2 ( x + 4 ) 2 e x d x = \displaystyle\int \dfrac{x+2}{(x+4)^2}\,e^x\,dx = ∫ ( x + 4 ) 2 x + 2 e x d x = A. e x ⋅ x x + 4 + c \dfrac{e^x \cdot x}{x+4} + c x + 4 e x ⋅ x + c B. e x ( x + 2 ) x + 4 + c \dfrac{e^x(x+2)}{x+4} + c x + 4 e x ( x + 2 ) + c C. e x ( x − 2 ) x + 4 + c \dfrac{e^x(x-2)}{x+4} + c x + 4 e x ( x − 2 ) + c D. e x ⋅ 2 x x + 4 + c \dfrac{e^x \cdot 2x}{x+4} + c x + 4 e x ⋅ 2 x + c Tap an option to check your answer.
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Question 2 3 May 2023 S1
145 The value of ∫ ( x − 1 ) e x ( x + 1 ) 3 d x \int\frac{(x-1)e^x}{(x+1)^3}\,dx ∫ ( x + 1 ) 3 ( x − 1 ) e x d x is equal to A. e x x + 1 + c \frac{e^x}{x+1}+c x + 1 e x + c B. e x ( x + 1 ) 2 + c \frac{e^x}{(x+1)^2}+c ( x + 1 ) 2 e x + c C. − e x x + 1 + c -\frac{e^x}{x+1}+c − x + 1 e x + c D. − e x ( x + 1 ) 2 + c -\frac{e^x}{(x+1)^2}+c − ( x + 1 ) 2 e x + c Tap an option to check your answer.
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Question 3 9 May 2023 S1
139 The value of I = ∫ ( x − 1 ) e x ( x + 1 ) 3 d x I=\int\frac{(x-1)e^x}{(x+1)^3}\,dx I = ∫ ( x + 1 ) 3 ( x − 1 ) e x d x is A. − e x ( x + 1 ) 2 + C -\frac{e^x}{(x+1)^2}+C − ( x + 1 ) 2 e x + C B. − x e x ( x + 1 ) 2 + C -\frac{xe^x}{(x+1)^2}+C − ( x + 1 ) 2 x e x + C C. x e x ( x + 1 ) 2 + C \frac{xe^x}{(x+1)^2}+C ( x + 1 ) 2 x e x + C D. e x ( x + 1 ) 2 + C \frac{e^x}{(x+1)^2}+C ( x + 1 ) 2 e x + C Tap an option to check your answer.
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Question 4 13 May 2024 S2
134 ∫ x − 3 ( x − 1 ) 3 e x d x = \int\frac{x-3}{(x-1)^3}e^x\,dx= ∫ ( x − 1 ) 3 x − 3 e x d x = A. e x 1 ( x − 1 ) 2 + c e^x\frac{1}{(x-1)^2}+c e x ( x − 1 ) 2 1 + c , where c is constant of integration B. e x 1 x − 1 + c e^x\frac{1}{x-1}+c e x x − 1 1 + c , where c is constant of integration C. e x ( x − 1 ) 2 + c e^x(x-1)^2+c e x ( x − 1 ) 2 + c , where c is constant of integration D. e x ( x − 1 ) 3 + c e^x(x-1)^3+c e x ( x − 1 ) 3 + c , where c is constant of integration Tap an option to check your answer.
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Question 5 14 May 2024 S2
126 The value of ∫ e x ( x 2 + 4 x + 4 ) ( x + 4 ) 2 d x \int \frac{e^x(x^2+4x+4)}{(x+4)^2}\,dx ∫ ( x + 4 ) 2 e x ( x 2 + 4 x + 4 ) d x is A. e x x x + 4 + c e^x\frac{x}{x+4} + c e x x + 4 x + c B. e x 4 x + 4 + c e^x\frac{4}{x+4} + c e x x + 4 4 + c C. e x x ( x + 4 ) 2 + c \frac{e^x x}{(x+4)^2} + c ( x + 4 ) 2 e x x + c D. e x 4 ( x + 4 ) 2 + c \frac{e^x 4}{(x+4)^2} + c ( x + 4 ) 2 e x 4 + c Tap an option to check your answer.
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Question 6 20 Apr 2025 S2
132 ∫ e x ( x − 1 ) ( x + 1 ) 3 d x = \int e^{x}\frac{(x- 1)}{(x+ 1)^{3}}\text{ }dx= ∫ e x ( x + 1 ) 3 ( x − 1 ) d x = A. e x ( x + 1 ) 2 + c e^{x}(x + 1)^{2} + c e x ( x + 1 ) 2 + c , where c is the constant of integration B. e x ( x + 1 ) 3 + c \ e^{x}(x + 1)^{3} + c e x ( x + 1 ) 3 + c , where c is the constant of integration C. e x ( x + 1 ) 2 + c \frac{e^{x}}{(x + 1)^{2}} + c ( x + 1 ) 2 e x + c , where c is the constant of integration D. e x ( x + 1 ) 3 + c \frac{e^{x}}{(x + 1)^{3}} + c ( x + 1 ) 3 e x + c , where c is the constant of integration Tap an option to check your answer.
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Question 7 25 Apr 2025 S1
114 ∫ e x ( x + 5 ( x + 6 ) 2 ) d x \int e^{x}\left( \frac{x+ 5}{(x+ 6)^{2}} \right)dx ∫ e x ( ( x + 6 ) 2 x + 5 ) d x is A. e x ( x + 6 ) 2 + c \frac{e^{x}}{(x + 6)^{2}} + c ( x + 6 ) 2 e x + c , where c is the constant of integration. B. e x x + 5 + c \frac{e^{x}}{x + 5} + c x + 5 e x + c , where c c c is the constant of integration. C. e x ( x + 5 ) 2 + c \frac{e^{x}}{(x + 5)^{2}} + c ( x + 5 ) 2 e x + c , where c is the constant of integration. D. e x x + 6 + c \frac{e^{x}}{x + 6} + c x + 6 e x + c , where c is the constant of integration. Tap an option to check your answer.
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