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Solve given integrals by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.

x4-32+3x2dx

Short Answer

Expert verified

x3929x23546tan162x+C

Step by step solution

01

Step1. Given Information

The integral is as follows.

x432+3x2dx

The objective is to solve the integral.

02

Step2. Long division

The polynomial long division method is calculated below.

13x2293x2+2x43x4+23x223x2323x249239

The expression is in the form ofx432+3x2=x2329+2393x2+2.

03

Step3. Solution

The integral is solved below.

x432+3x2dx=x2329+2393x2+2dx=x23dx29dx23913x2+2dx=x3929x23546tan162x+C

Therefore, the value isx3929x23546tan162x+C

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