MCQs of Integrals

Integrals MCQs

Showing 111 to 120 out of 421 Questions

111.

\int \frac{x \sqrt{x}}{2 x^{5} + 5}

dx = _____ + c

(a) $\frac{\sqrt{2}}{5} \tan^{- 1} (\frac{\sqrt{2} x^{\frac{5}{2}}}{\sqrt{5}})$

(b) $\frac{\sqrt{2}}{5 \sqrt{5}} \tan^{- 1} (\frac{\sqrt{2} x^{\frac{5}{2}}}{\sqrt{5}})$

(c) $\frac{2}{5 \sqrt{5}} \tan^{- 1} (\frac{\sqrt{2} x^{\frac{5}{2}}}{\sqrt{5}})$

(d) none of these.

112.

\int e^{3 \log x} {(x^{4} + 1)}^{- 1}

dx = _____

(a) $\frac{1}{4} \log (x^{4} + 1) + c$

(b) $- \log (x^{4} + 1) + c$

(c) $\log (x^{4} + 1) + c$

(d) none of these.

113.

\int \frac{\cos \sqrt{x}}{\sqrt{x}}

= _____ + c

(a) $2 \cos \sqrt{x}$

(b) $\sqrt{\frac{\cos x}{2}}$

(c) $\sin \sqrt{x}$

(d) $2 \sin \sqrt{x}$

114.

\int 5^{5^{x}} 5^{x}

dx = _____ + c

(a) ${(\log_{e} 5)}^{2} 5^{5^{x}}$

(b) $5^{5^{x}} (\log_{e} 5)$

(c) $5^{5^{x}}$

(d) $\frac{5^{5^{x}}}{{(\log_{e} 5)}^{2}}$

115.

\int \frac{{(\sin x)}^{\frac{5}{2}}}{{(\cos x)}^{\frac{9}{2}}}

dx = _____ + c

(a) $- \frac{2}{5} {(\tan x)}^{\frac{5}{2}}$

(b) $\frac{2}{5} {(\tan x)}^{\frac{5}{2}}$

(c) $\frac{2}{7} {(\tan x)}^{\frac{7}{2}}$

(d) $- \frac{2}{7} {(\tan x)}^{\frac{7}{2}}$

116.

\int \frac{x^{3}}{x^{8} + 1}

dx = _____ + c

(a) $\frac{1}{4} \tan^{- 1} (x^{4})$

(b) $\tan^{- 1} (x^{4})$

(c) $\log |1 + x^{4}|$

(d) $\frac{1}{4} \log |1 + x^{4}|$

117.

\int x^{n x} (1 + \log x)

dx = _____ + c , $(n \neq 0)$

(a) $\frac{x^{(x - 1) x}}{n - 1}$

(b) $\frac{x^{(n - 1) x}}{n - 1}$

(c) $\frac{x^{n x}}{n}$

(d) none of these.

118.

\int \frac{d x}{(2 x - 7) \sqrt{x^{2} - 7 x + 12}}

= _____ + c , 2x>7

(a) $2 s e c^{- 1} (2 x - 7)$

(b) $s e c^{- 1} (2 x - 7)$

(c) $\frac{1}{2} s e c^{- 1} (2 x - 7)$

(d) none of these.

119.

\int \frac{3 \tan \frac{x}{3} - \tan^{3} \frac{x}{3}}{1 - 3 \tan^{2} \frac{x}{3}}

dx = _____

(a) $- \log |s e c x| + c$

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

(c) $s e c^{2} x + c$

(d) $\log |\tan x| + c$

120.

\int \frac{2 x}{(1 - x^{2}) \sqrt{x^{4} - 1}}

dx = _____ + c

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

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

(c) $\sqrt{x^{4} - 1}$

(d) none of these.

Showing 111 to 120 out of 421 Questions