MCQs of Integrals

Showing 271 to 280 out of 421 Questions

271.

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

= _____ + c

272.

\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)	$\frac{(5 x + 3)}{10} \sqrt{25 x^{2} - 30 x + 34} - \frac{5}{10} \log \|(5 x - 3) + \sqrt{25 x^{2} - 30 x + 34}\|$

273.

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

= _____ + c

274.

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

= _____ + c

275.

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

= _____ + c

276.

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

= _____ + c

277.

\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)	$\frac{\cos x}{2} \sqrt{4 - \cos^{2} x} + 2 \sin^{- 1} (\frac{\cos x}{2})$

278.

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

= _____ + c

279.

\int \frac{e^{5 \log x} - e^{3 \log x}}{e^{4 \log x} - e^{2 \log x}} d x

= _____ + c

280.

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

= _____ + c

Showing 271 to 280 out of 421 Questions