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#### GreenGoblin

##### Member

- Feb 22, 2012

- 68

Please help me to evaluate the following integrals:

1) $\int\frac{x^{4}+1}{x^{2}+1}dx$

I recognise the form of $x^{2}+1$ in the denominator corresponds to an inverse tangent derivative. But how would I deal with the numerator in this respect?

2) $\int\frac{1}{x^{2}+x-6}dx$

I believe this involves completing the square, I made the first step of doing this, rearranging to $\int\frac{1}{(x + \frac{1}{2})^{2}-\frac{25}{4}}dx$, but I am not entirely sure of the exact integration formula corresponding to this. I observe 25 and 4 are clearly both squares too so I assume this problem set this up intentionally, and this bears a relevance for the remainder of the problem.

Gracias,

GreenGoblin

1) $\int\frac{x^{4}+1}{x^{2}+1}dx$

I recognise the form of $x^{2}+1$ in the denominator corresponds to an inverse tangent derivative. But how would I deal with the numerator in this respect?

2) $\int\frac{1}{x^{2}+x-6}dx$

I believe this involves completing the square, I made the first step of doing this, rearranging to $\int\frac{1}{(x + \frac{1}{2})^{2}-\frac{25}{4}}dx$, but I am not entirely sure of the exact integration formula corresponding to this. I observe 25 and 4 are clearly both squares too so I assume this problem set this up intentionally, and this bears a relevance for the remainder of the problem.

Gracias,

GreenGoblin

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