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Question

Solve
x+2x2+2x+3dx

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Solution

x+2x2+2x+3dx
=x+1x2+2x+3dx+1x2+2x+3dx

Let x2+2x+3=t
=2x+2=dtdx
=2(x+1)=dtdx
=(x+1)dx=dt2
=dt2t+1x2+2x+11+3dx
=12⎢ ⎢ ⎢t1/2+112+1⎥ ⎥ ⎥+1(x+1)2+(2)2dx
=12t1/212+log(x+1+x2+2x+3)
=t1/2+log(x+1+x2+2x+3)
=x2+2x+3+log(x+1+x2+2x+3)+c
Hence, the answer is x2+2x+3+log(x+1+x2+2x+3)+c.


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