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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

If

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

, then

f(x)=

View answer and explanation

Correct option: A

\tan ^{-1}(x+1)

Option A,

\tan^{-1}(x+1)

, is the correct answer because the integral of

\frac{1}{x^2+2x+2}

is indeed

\tan^{-1}(x+1) + C

.

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

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\int\limits_{0}^{t^2} x f(x) d x=\frac{2}{5} t^5

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}

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{C}

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\int \frac{x^7}{\left(1-x^2\right)^5} d x

\int \,\frac{{a{x^3} + \,\,b{x^2} + c}}{{{x^4}}}\;\,dx