Pls help solve integral w steps \int\limits (x)/(x^2-8x+32) dx

Question

Pls help solve integral w steps


`\int\limits (x)/(x^2-8x+32) dx`

Answer 1

`\int\limits {(x)/(x^2-8x+32)} \, dx=(1)/(2)ln|(x-4)^2+16|+4tan^(-1)((1)/(16)(x-4))`

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Explanation:

lol. why is this problem so hard.

but basically, my first instinct when seeing a fraction was to use partial fraction, but that failed.

So next option was to complete the square. After completing the square, I used u-substitution and seperated my integral into 2 different fractions. Both of which requires you to do double substitution.

Hopefully you already know the integral for ln|x| and tan⁻¹(x) which are used in solving this problem.