`int (x^2 + 1 + 1/(x^2 + 1)) dx` Find the general indefinite integral.

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Chapter 5, 5.4 - Problem 12 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`int(x^2+1+1/(x^2+1))dx`

apply the sum rule,

`=intx^2dx+int1dx+int1/(x^2+1)dx`

To evaluate the above integrals, we know that,

`intx^ndx=x^(n+1)/(n+1)`  and `int1/(x^2+1)dx=arctan(x)`

using above,

`=x^3/3+x+arctan(x)+C`  where C is constant

 

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