MCQs of Integrals

Integrals MCQs

Showing 161 to 170 out of 403 Questions

161.

\int \frac{d^{2}}{d x^{2}} (\tan^{- 1} x) d x =

_____ + c

(a)	$\frac{1}{1 + x^{2}}$
(b)	tan^-1x
(c)	$x \tan^{- 1} x - \frac{1}{2} \log (1 + x^{2})$
(d)	None of these

162.

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

= _____ + c

(a)	$e^{\frac{x}{\sqrt{2}}} \sin (\frac{x}{\sqrt{2}} - \frac{π}{4})$
(b)	$e^{\frac{x}{\sqrt{2}}} \sin (\frac{x}{\sqrt{2}} + \frac{π}{4})$
(c)	$e^{\frac{x}{\sqrt{2}}} \cos (\frac{x}{\sqrt{2}} + \frac{π}{4})$
(d)	None of these

163.

\int e^{x} (\frac{x - 4}{x^{5}}) d x =

_____ + c

(a)	$\frac{e^{x}}{x^{5}}$
(b)	$- \frac{e^{x}}{x^{4}}$
(c)	$\frac{e^{x}}{x^{4}}$
(d)	$- \frac{e^{x}}{x^{5}}$

164.

\int \frac{e^{x}}{x} \log (e x^{x}) d x =

_____ + c

(a)	e^x logx^x
(b)	$\frac{e^{x}}{x} \log x^{x}$
(c)	e^x logx
(d)	None of these

165.

\int e^{x} \cos x (1 + \tan x) d x =

_____ + c

(a)	e^xsecx
(b)	e^xtanx
(c)	e^xcosx
(d)	e^xsinx

166.

\int \frac{\sin^{2} x}{\cos^{6} x}

dx = _____ + c

(a) $\frac{1}{3} \tan^{3} x + \frac{1}{5} \tan^{5} x$

(b) $\frac{1}{3} c o t^{3} x + \frac{1}{5} c o t^{5} x$

(c) $\frac{1}{3} \sin^{3} x + \frac{1}{3} \cos^{7} x$

(d) none of these.

167.

\int \frac{\cos x + x \sin x}{x^{2} + x \cos x}

dx =_____ + c

(a) $\log |x^{2} + x \cos x|$

(b) $\log |x + x \cos x|$

(c) $\log |\frac{x}{x + \cos x}|$

(d) $\log |\frac{x + \cos x}{x}|$

168.

\int \sqrt{\cos e c x + 1}

dx = _____ + c

(a) $\tan^{- 1} \sqrt{\cos e c x - 1}$

(b) $2 \tan^{- 1} \sqrt{\cos e c x - 1}$

(c) $- \tan^{- 1} \sqrt{\cos e c x - 1}$

(d) $- 2 \tan^{- 1} \sqrt{\cos e c x - 1}$

169.

\int \frac{e^{x} - 1}{e^{x} + 1}

dx = _____ + c

(a) $\frac{1}{2} \log |e^{\frac{x}{2}} + e^{\frac{- x}{2}}|$

(b) $2 \log |e^{\frac{x}{2}} + e^{\frac{- x}{2}}|$

(c) $2 \log |e^{x} + 1|$

(d) none of these.

170.

\int \frac{{(\sqrt{1 + x^{2}} + x)}^{n}}{\sqrt{1 + x^{2}}}

dx = _____ + c

(a) $\frac{1}{n} {(\sqrt{1 + x^{2}} + x)}^{n}$

(b) $\frac{1}{x} {(\sqrt{1 + x^{2}} + x)}^{n}$

(c) ${(\sqrt{1 + x^{2}} + x)}^{n + 1}$

(d) none of these.

Showing 161 to 170 out of 403 Questions