`int (x + 4)/(x^2 + 2x + 5) dx` Evaluate the integral

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Integrate `int(x+4)/(x^2+2x+5)dx`



Integrate the first integral on the left side of the equation using the u-substitution method.

Let `u=x^2+2x+5`








The second integral on the left side will match the form 

`intdx/(x^2+a^2)=1/atan^-1(x/a)+C` after you complete the square in the denominator.








The final answer is: 




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