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$\int \frac{p x^{p + 2 q - 1} - q x^{q - 1}}{x^{2 p + 2 q} + 2 x^{p + q} + 1} d x =$

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detailed solution

Correct option is C

∫pxp+2q−1−qxq−1xp+q+12dxDividing numerator and denominator by x2q=∫pxp−1−qx−q−1xp+x−q2dxput xp+x−q =t⇒pxp−1−qx−q−1dx=dt=∫dtt2=−1t+c=−1xp+x−q+c=−xqxp+q+1+c

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∫ pxp+2q-1-qxq-1x2p+2q+2xp+q+1dx=

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$\int \frac{p x^{p + 2 q - 1} - q x^{q - 1}}{x^{2 p + 2 q} + 2 x^{p + q} + 1} d x =$