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BITSAT 2023Paper 1

Exam: BITSAT
Year: 2023
Paper: Paper 1
Subject: Mathematics
Chapter: Indefinite Integration

BITSAT 2023 · Paper 1 · Mathematics · Indefinite Integration

∫ (x+3)/((x+4)^2) e^x d x is equal to

\int \frac{x+3}{(x+4)^2} e^x d x

is equal to

Options

A $e^x\left(\frac{1}{x+4}\right)+C$
B $e^{-x}\left(\frac{1}{x+4}\right)+C$
C $e^{-x}\left(\frac{1}{x-4}\right)+C$
D $e^{2 x}\left(\frac{1}{x-4}\right)+C$

Correct answer

A. $e^x\left(\frac{1}{x+4}\right)+C$

Step-by-step solution

Suppose,

I=\int \frac{x+3}{(x+4)^2} e^x d x=\int \frac{(x+4) 1}{(x+4)^2} e^x d x<br />

=\int \frac{e^x}{(x+4)}-\int \frac{e^x}{(x+4)^2} d x

<br />

=\int e^x\left(\frac{1}{(x+4)}-\frac{1}{(x+4)^2}\right) d x

<br />

=e^x \frac{1}{(x+4)}+C

<br />\left[\int e^x \left\{f(x)+f^{\prime}(x)\right\}

d x=e^x f(x)+C\right]

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