# What is #int (2x)/(x^2+6x+13) dx#?

A marginally distinct method:

Divide the percentage:

This provides us with

Finish the square in the denominator for the subsequent integral.

This should be similar to the arctangent integral.

Putting everything together,

When we combine this with the earlier-derived expression, we find that the original integral equals

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The integral of ( \frac{2x}{x^2+6x+13} ) with respect to ( x ) is ( \ln|x^2+6x+13| + C ), where ( C ) is the constant of integration.

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