The correct option is D e^x( x+1)+c ∫ e^x(cot x cot^2x)dx ∫ e^x ( (cot x+1) (1+cot^2x) )dx ∫ e^x [ (cot x+1) cosec^2x ]dx It is in the fo ...

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Special Integrals - 1

∫ excotx-cot2...

Question

$\int e^{x} (c o t x - c o t^{2} x) d x =$

(cot x) + c

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e^{x} (1 - {cot}^{2} x) + c

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e^{x} {cot}^{2} x + c

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e^{x} (cot x + 1) + c

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Solution

The correct option is D $e^{x} (cot x + 1) + c$
$\int e^{x} (c o t x - c o t^{2} x) d x$
$\int e^{x} ((c o t x + 1) - (1 + c o t^{2} x)) d x$
$\int e^{x} [(c o t x + 1) - c o s e c^{2} x] d x$

It is in the form of

$\int e^{x} [f (x) + f^{^{'}} (x)] d x = e^{x} f (x) + c$

$= e^{x} (c o t x + 1) + c$

Suggest Corrections

Similar questions

I

\int e^{x} (1 - cot x + {cot}^{2} x) d x = - e^{x} cot x + c

I I : \int e^{x} (\frac{1 + x log x}{x}) d x = e^{x} log x + c

\int e^{x} (1 - \cot x + \cot^{2} x) d x =

$\int e^{x} (\frac{1 - c o t x}{s i n x}) d x$

equals

A. − cot (ex^x) + C

B. tan (xe^x) + C

C. tan (e^x) + C

D. cot (e^x) + C

\int \frac{e^{x} (1 + x) d x}{{cos}^{2} (e^{x} x)}

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