# Math Help - Hard Integration help

1. ## Hard Integration help

Can you please solve this problems?

$\int\frac{x^4-x {dx}}{x^2-1}$
$\int\frac{e^{4y}}{e^{2y}+1}dy$
$\int\frac{dx}{(2x-1)[3-2 \ln (1-2x)]}$
$\int\frac{dx}{x(1-x^3)}$
$\int\frac{(3-4x)x dx}{\sqrt[3]{1-x}}$

Thanks in Advance

2. Originally Posted by Yuroichi
Can you please solve this problems?

$\int\frac{x^4-x {dx}}{x^2-1}$
$\int\frac{e^{4y}}{e^{2y}+1}dy$
$\int\frac{dx}{(2x-1)[3-2 \ln (1-2x)]}$
$\int\frac{dx}{x(1-x^3)}$
$\int\frac{(3-4x)x dx}{\sqrt[3]{1-x}}$

Thanks in Advance
1. Note that $\frac{x^4-x}{x^2-1} = \frac{x(x - 1)(x^2 + x + 1)}{(x - 1)(x + 1)} = \frac{x^3 + x^2 + x}{x + 1} = x^2 + 1 - \frac{1}{x + 1}$.

2. Start by substituting $u = e^{2y}$.

3. Start by substituting $u = \ln (1 - 2x)$.

4. Completely factorise the denominator and then use a partial fraction decomposition.

5. Start by substituting $u^3 = 1 - x$.

If you need more help, please post your working and state where you get stuck.