# Thread: Evaluating a definite integral

1. ## Evaluating a definite integral

$\displaystyle \int [cos(x)\cdot e^{2sin(x))}+\pi \cdot cos(4x)+\sqrt{2}\cdot x^{1/3}+\frac{1}{x}] dx$

undefinite integral btw , I normally know how to do these, but the multiplication inside the integration is confusing me

2. I agree ... your latex skills leave much to be desired.

$\displaystyle \int \cos{x} \cdot e^{2\sin{x}} + \pi\cos(4x) + x^{\frac{3}{2}} + \frac{1}{x} \, dx$

3. Originally Posted by skeeter
I agree ... your latex skills leave much to be desired.

$\displaystyle \int \cos{x} \cdot e^{2\sin{x}} + \pi\cos(4x) + x^{\frac{3}{2}} + \frac{1}{x} \, dx$
$\displaystyle \int [cos(x)\cdot e^{2sin(x))}+\pi \cdot cos(4x)+\sqrt{2}\cdot x^{1/3}+\frac{1}{x}] dx$
$\displaystyle \frac{e^{2\sin{x}}}{2} + \frac{\pi\sin(4x)}{4} + \frac{3\sqrt{2}}{4} x^{\frac{4}{3}} + \ln|x| + C$
$\displaystyle \frac{e^{2\sin{x}}}{2} + \frac{\pi\sin(4x)}{4} + \frac{3\sqrt{2}}{4} x^{\frac{4}{3}} + \ln|x| + C$
i see how you get your $\displaystyle ln|x|+C$ , but I just don't get how you get the rest, what happens when you multiply in an integration, could you do it step by step please ?