# How do you find the indefinite integral of #int (x^4+x-4)/(x^2+2)#?

The answer is

We need

Perform a polynomial long division

Therefore,

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To find the indefinite integral of ( \frac{x^4 + x - 4}{x^2 + 2} ), you can use polynomial long division to divide (x^4 + x - 4) by (x^2 + 2), then integrate the resulting expression. After performing polynomial long division, the integral becomes:

[ \int \left(x^2 - 2 + \frac{4x - 8}{x^2 + 2}\right) , dx ]

The integral of (x^2 - 2) is ( \frac{1}{3}x^3 - 2x ). To integrate ( \frac{4x - 8}{x^2 + 2} ), you can perform a substitution or use another method such as partial fraction decomposition.

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