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$\log |\sec ({xe}^{x})| + C$

$\int \frac{(1 + x) e^{x}}{\cot ({xe}^{x})} dx$

$Put {xe}^{x} = t \Rightarrow ({xe}^{x} + e^{x}) dx = dt \Rightarrow (x + 1) e^{x} dx = dt$

$∴ I = \int \frac{dt}{\cot (t)} = \int \tan (t) dt = \log |\sec (t)| + C Again, put t = {xe}^{x} \Rightarrow I = \log |\sec ({xe}^{x})| + C$

232.

$\int \frac{x^{5}}{\sqrt{1 + x^{3}}} dx$ is equal to

233.

$\int \frac{4 e^{x}}{2 e^{x} - 5 e^{- x}} dx$ is equal to

234.

$\int {(\sqrt{x} + \frac{1}{\sqrt{x}})}^{2} dx$ is equal to

235.

$\int \frac{x^{n - 1}}{x^{2 n} + a^{2}} dx$ is equal to

236.

$\int \frac{{(x + 1)}^{2}}{x (x^{2} + 1)} dx$ is equal to

237.

$\int \frac{1}{xlog (x^{2})} dx$ is equal to

238.

$\int_{0}^{1} \frac{1}{(x^{2} + 16) (x^{2} + 25)} dx$ is equal to

$\frac{1}{5} [\frac{1}{4} \tan^{- 1} (\frac{1}{4}) - \frac{1}{5} \tan^{- 1} (\frac{1}{5})]$
$\frac{1}{9} [\frac{1}{4} \tan^{- 1} (\frac{1}{4}) - \frac{1}{5} \tan^{- 1} (\frac{1}{5})]$
$\frac{1}{4} [\frac{1}{4} \tan^{- 1} (\frac{1}{4}) - \frac{1}{5} \tan^{- 1} (\frac{1}{5})]$
$\frac{1}{9} [\frac{1}{5} \tan^{- 1} (\frac{1}{4}) - \frac{1}{4} \tan^{- 1} (\frac{1}{5})]$