Could someone please show me step-by-step how to solve this integral?

Question

anonymous · Answer

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anonymous · Answer

what you need to do to solve an integral like this is first do a polynomial division and then use partial fraction decomposition, have you covered those topics already?

anonymous · Answer

I'm so sorry. I think I've completely forgotten what partial fraction decomposition is. O.o this sounds like it's going to be really hard...

anonymous · Answer

in fact it's not an easy integral for sure yes. Have you been introduced to inverse trig substitution methods to solve integrals?

anonymous · Answer

$$\Large \frac{x^2+1}{x^2+7}= 1- \frac{6}{x^2+7}  \text{ by longhand division }$$

anonymous · Answer

apparently the first integral is easy, the second one is a bit harder to integrate. It requires a trigonometric substitution.

anonymous · Answer

I know how to solve a trigonometric substitution integral, I just never would have figured out to do polynomial division to split the fraction into two separate integrals O.o I appreciate it- thank you

anonymous · Answer

oh ok, great then you're well prepared to solve the integral above :-)