-ex 1- x- 2 x d x-a ex x-Cb -ex x-Cc excosec x-Cd -excosec x-C

(b) minus;ex cot x + C Let #160;I= #8747;ex1 cot #160;x+cot2xdx #160; #160; #160; #160; #160; #160; #160;= #8747;excosec2x cot #160; ...

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Byju's Answer

Standard XII

Mathematics

Implicit Differentiation

∫ex 1- x+ 2 x...

Question

$\int e^{x} (1 - \cot x + \cot^{2} x) d x =$
(a) e^x cot x + C
(b) −e^x cot x + C
(c) e^x cosec x + C
(d) −e^x cosec x + C

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Solution

(b) −e^x cot x + C

$Let I = \int e^{x} (1 - \cot x + \cot^{2} x) d x = \int e^{x} ({cosec}^{2} x - \cot x) d x As we know that \int e \{f (x) + f'^{x} (x)\} = e^{x} f (x) + C ∴ I = - e^{x} \cot x + C$

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Similar questions

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

equals

A. − cot (ex^x) + C

B. tan (xe^x) + C

C. tan (e^x) + C

D. cot (e^x) + C

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-cot x+cot2 x dx= (a) ex cot x + C (b) −ex cot x + C (c) ex cosec x + C (d) −ex cosec x + C

(b) −ex cot x + C Let I=∫ex1-cot x+cot2xdx =∫excosec2x-cot xdxAs we know that ∫efx+f'xx=exfx+C∴ I=-ex cot x+C

$\int e^{x} (1 - \cot x + \cot^{2} x) d x =$
(a) e^x cot x + C
(b) −e^x cot x + C
(c) e^x cosec x + C
(d) −e^x cosec x + C

(b) −e^x cot x + C

$Let I = \int e^{x} (1 - \cot x + \cot^{2} x) d x = \int e^{x} ({cosec}^{2} x - \cot x) d x As we know that \int e \{f (x) + f'^{x} (x)\} = e^{x} f (x) + C ∴ I = - e^{x} \cot x + C$