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Evaluate `intsqrt(1+y^2)*2ydy` |
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Answer» Let `I=intsqrt(1+y^2)*2ydy` Let `u=1+y^2`, then `du=2ydy`. `I=intu^(1//2)du` `=(u^((1//2)+1))/((1//2)+1)` [Integrate, using rule no. 3 with `n=1//2`] `=2/3u^(3//2)+C` [Simpler form] `2/3(1+y^2)^(3//2)+C` [Replace u by `1+y^2`] |
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