Question-132647

Question Number 132647 by aurpeyz last updated on 15/Feb/21

Answered by Dwaipayan Shikari last updated on 15/Feb/21

\int \frac{1}{\sqrt{x} (\sqrt{x} + 7)} d x x = t^{2}

= 2 \int \frac{1}{t + 7} d t = 2 l o g (t + 7) + C = l o g {(\sqrt{x} + 7)}^{2} + C

Answered by EDWIN88 last updated on 15/Feb/21

let \sqrt{x} + 7 = u and x = {(u - 7)}^{2}

I = \int \frac{2 (u - 7)}{(u - 7) u} du = \int \frac{2}{u} du = 2 \ln u + c

I = 2 \ln (\sqrt{x} + 7) + c

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