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Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

xx2+1dx

Short Answer

Expert verified

The solution of the integral is13x2+132+C.

Step by step solution

01

Step 1. Given Information.

The given integral isxx2+1dx.

02

Step 2. Solve. 

To solve the integral, let u=x2+1, so derivation of uis du=2xdx.

Thus, substitute u into the original integral,

xx2+1dx=12u-1uduu-1=12udu=1223u32+C=13u32+C

Substitute back uin the above equation,

=13x2+132+C

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