- #1
karush
Gold Member
MHB
- 3,269
- 5
$$\displaystyle
I=\int \frac{3{x}^{2}-{x}^{2}+6x-4}{({x}^{2}+1)({x}^{2}+2)} \\
=\frac{2}{3}\ln\left({x}^{2}+1\right)-3\arctan\left({x}\right)
+\sqrt{2}\arctan\left({x/\sqrt{2}}\right)+C$$
Was going to take this a step at a time
so by observation this looks like an expasion
The way the answer looks
I=\int \frac{3{x}^{2}-{x}^{2}+6x-4}{({x}^{2}+1)({x}^{2}+2)} \\
=\frac{2}{3}\ln\left({x}^{2}+1\right)-3\arctan\left({x}\right)
+\sqrt{2}\arctan\left({x/\sqrt{2}}\right)+C$$
Was going to take this a step at a time
so by observation this looks like an expasion
The way the answer looks
Last edited: