What is the integral int (x^2+1)(x^3+3x)^4 dx

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What is the integral int (x^2+1)(x^3+3x)^4 dx?

`int (x^2+1)(x^3+3x)^4 dx`

Use U-substitution to solve this.

`U=x^3+3x `

Take the derivative.  Notice that there is a common factor of three!

`dU= 3x^2 +3 dx= 3(x^2+1) dx`

Divide by three on both sides, and then we will see that we can plug in `(x^2+1) dx`

`1/3 dU = (x^2+1) dx`

Now that we know  and , substitute these back to the integral.


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