MCQs of Integrals

Showing 261 to 270 out of 403 Questions

261.

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

= _____ + c

262.

\int \log_{|a|} x d x

= _____ + c (જ્યાં a < -e)

263.

\int e^{3 x} \sin 2 x d x

= _____ + c

264.

\int {(25 x^{2} - 30 x + 34)}^{\frac{1}{2}} d x

= _____ + c

(a)	$\frac{(5 x - 3)}{10} \sqrt{25 x^{2} - 30 x + 34} + \frac{5}{10} \sin^{- 1} (\frac{5 x - 3}{5})$
(b)	$\frac{(5 x - 3)}{10} \sqrt{25 x^{2} - 30 x + 34} + \frac{25}{10} \log \|(5 x - 3) + \sqrt{25 x^{2} - 30 x + 34}\|$
(c)	$\frac{(5 x + 3)}{10} \sqrt{25 x^{2} - 30 x + 34} + \frac{5}{10} \log \|(5 x - 3) + \sqrt{25 x^{2} - 30 x + 34}\|$
(d)	$\frac{(5 x + 3)}{10} \sqrt{25 x^{2} - 30 x + 34} - \frac{5}{10} \log \|(5 x - 3) + \sqrt{25 x^{2} - 30 x + 34}\|$

265.

\int \frac{1}{x^{3}} \sin (\log x) d x

= _____ + c

266.

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

= _____ + c

267.

\int x^{4} e^{x} d x

= _____ + c

268.

\int \frac{x^{3} d x}{x^{2} + a^{2}}

= _____ + c

269.

\int \sin x \sqrt{4 - \cos^{2} x} d x

= _____ + c

(a)	$- \frac{\cos x}{2} \sqrt{4 - \cos^{2} x} + 2 \log \|x + \sqrt{4 - \cos^{2} x}\|$
(b)	$- \frac{\cos x}{2} \sqrt{4 - \cos^{2} x} + 2 \sin^{- 1} (\frac{\cos x}{2})$
(c)	$- \frac{\cos x}{2} \sqrt{4 - \cos^{2} x} - 2 \sin^{- 1} (\frac{\cos x}{2})$
(d)	$\frac{\cos x}{2} \sqrt{4 - \cos^{2} x} + 2 \sin^{- 1} (\frac{\cos x}{2})$

270.

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

= _____ + c

Showing 261 to 270 out of 403 Questions