Theorems on Integration

Q. $\int \frac{x^8+4}{x^4-2x^2+2}dx=$

1. $\frac{x^5}{5}-\frac{2x^3}{3}+2x+C$
2. $\frac{x^5}{5}-\frac{2x^3}{3}-2x+C$
3. $\frac{x^5}{5}+\frac{2x^3}{3}-2x+C$
4. $\frac{x^5}{5}+\frac{2x^3}{3}+2x+C$

Q.

$\int e^{ta{n}^{-1}x}(1+x+x^2).d\left(co{t}^{-1}x\right)$ is equal to

1. $-e^{ta{n}^{-1}x}+C$

2. $e^{ta{n}^{-1}x}+C$

3. $-x.e^{ta{n}^{-1}x}+C$

4. $x.e^{ta{n}^{-1}x}+C$