Question

integrate it by substitution

Answer 1

hope this will help you

Answer 2

Answer:

solution:-

$\implies \int \: \frac{x {}^{2} }{1 + x {}^{6} }dx$

can We be written as

$\implies \int \: \frac{x {}^{2} }{1 + (x {}^{3}) {}^{2} }$

let x^3=t

$\implies \: \frac{d}{dx} x {}^{3} = dt \\ \\ \implies \: 3x {}^{2} dx = dt \\ \\ \implies \: x {}^{2} dx = \frac{dt}{3}$

put value

$\implies \int \: \frac{1}{1 + t {}^{2} } \frac{dt}{3}$

$\implies \: \frac{1}{3} \tan {}^{ - 1} t$

put t value

$\implies \: \frac{1}{3} \tan {}^{ - 1} x {}^{3} + c$

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I hope it helps you