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QUESTION

Find $\ds\int x\left(1+x^2\right)^6\,dx$.

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ANSWER

$\ds\int x(1+x^2)^6\, dx=\frac{1}{14} (1+x^2)^7 +c\\ \{u=1+x^2,\
 du = 2 x dx,$ therefore $\ds I=\int \frac{1}{2} du (u^6)=\frac{u^7} {2(7)} +c\}$




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