- e x 1-cotx-sin x d xA- ex x-cB- excos e c x- cC- -excos e c x-cD- -ex x-c

The correct option is B ∫ e^x [cosec x + ( cosec x cot x)]dx =e^x(cosec x)+c ...

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Byju's Answer

Standard XII

Mathematics

Derivative of Standard Functions

∫ e x 1-cotx/...

Question

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

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Solution

The correct option is B

$\int e^{x} [c o s e c x + (- c o s e c x c o t x)] d x$

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

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Similar questions

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

(a) e^x cot x + C
(b) −e^x cot x + C
(c) e^x cosec x + C
(d) −e^x cosec x + C

equals

A. − cot (ex^x) + C

B. tan (xe^x) + C

C. tan (e^x) + C

D. cot (e^x) + C

Q. The value of

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

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

(a) $\frac{e^{x}}{x + 4} + C$

(b) $\frac{e^{x}}{x + 3} + C$

(c) $\frac{1}{{(x + 4)}^{2}} + C$

(d) $\frac{e^{x}}{{(x + 4)}^{2}} + C$

$\int \frac{e^{x} (x - 1) (x - l n x)}{x^{2}} d x$ is equal to

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∫ex(1−cotxsinx)dx

The correct option is B ∫ex[cosecx+(−cosecxcotx)]dx =ex(cosecx)+c

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

The correct option is B

$\int e^{x} [c o s e c x + (- c o s e c x c o t x)] d x$

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