$\int e^x\left(1-\cot x+\cot ^2 x\right)

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

$\int e^x\left(1-\cot x+\cot ^2 x\right) d x=$

Options:

$e^x \cot x+C$

$-e^x \cot x+C$

$e^x cosec~ x+C$

$-e^x cosec~ x+C$

Correct Answer:

$-e^x \cot x+C$

Explanation:

We have,

$I =\int e^x\left(1-\cot x+\cot ^2 x\right) d x=\int e^x\left(1+\cot ^2 x-\cot x\right) d x$

$\Rightarrow I =\int e^x\left(-\cot x+cosec^2 x\right) d x=-e^x \cot x+C$