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Question

Integrate:
1x+xdx=

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Solution

1x+xdx⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢putx=udiff.w.r.t.x,12xdx=du12udx=dudx=2udu⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥1u+u2.2udu2uu(u+1)du21u+1du=2log(u+1)2log(x+1)+c

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