\[\frac{1}{2}\log(1 + \sin^{2}x) + c] | MATH - INTEGRATION BY SUBSTITUTION | SolveeIt

$\frac{1}{2}\log(1 + \sin^{2}x) + c$

$\tan^{- 1}(\sin x) + c$

$\int_{}^{}{\frac{x^{3}}{\sqrt{x^{2} + 2}}dx =}$

$\frac{1}{3}(x^{2} + 2)^{3/2} + 2(x^{2} + 2)^{1/2} + c$

$\frac{1}{3}(x^{2} + 2)^{3/2} - 2(x^{2} + 2)^{1/2} + c$

Answer

$\int_{}^{}{\frac{x^{3}}{\sqrt{x^{2} + 2}}dx =}$

Explanation

$\frac{\sin^{4}x\cos^{2}x}{8} + c$

Now put $\frac{\sin^{4}x}{4} + c$

then it reduces to $\frac{\sin^{2}x}{2} + c$

$4\sin^{4}x + c$ .

Question: \[\frac{1}{2}\log(1 + \sin^{2}x) + c\]...