JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int x^5 \cdot e^{x^2} d x=

View answer and explanation

Correct option: A

\frac{1}{2} x^4 e^{x^2}-x^2 e^{x^2}+e^{x^2}+c

Option A (

\frac{1}{2} x^4 e^{x^2}-x^2 e^{x^2}+e^{x^2}+c

) is correct because substituting

x^2 = t

simplifies the integral, and integration by parts yields the correct result.

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\int \sin ^5 x \cos ^4 x d x=

f(x)

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f\left(\frac{4}{25}\right)

\int \frac{1-7 \cos ^2 x}{\sin ^7 x \cos ^2 x} d x=\frac{f(x)}{\sin ^7 x}+C

\int {e}^{{x}^2}\left(2-\frac{1}{{x}^2}\right) {de}={e}^{{x}^2} {f}({x})+{C}

{f}\left(\frac{1}{2}\right)=2

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{C}

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