Help I'm in college and have forgotten everything

[KingNothing]

Hi. I am in college and have forgotten everything about how to solve indefinite integrals.

Even very simple problems give me trouble, such as:

int( y^3 * sqrt(2y^4 - 1) ) dy

So how in the world do you find the answer? The Antiderivative? Please go through this step-by-step, I need a good jumpstart to get myself in the right frame of mind again.

 

[courtrigrad]

So you have $$\int y^{3}\sqrt{2y^{4}-1} dy$$. Let $$u = 2y^{4} -1$$, then $$du = 8y^{3} dy$$. But there is only a $$y^{3} dy$$ available so we have to multiply the integral by $$\frac{1}{8}$$:

$$\frac{1}{8} \int u^{\frac{1}{2}} du = \frac{1}{12}(2y^{4}-1)^\frac{3}{2} + C$$