Как решать такие интегралы?

Решите задачу:

$\int {x^6+cosx+e^x} \, dx = \int x^6dx + \int cosxdx+\int e^xdx=\\=\frac{x^7}{7}+sinx+e^x+C$

$\int cos(2x-\frac{\pi}{8})dx=\frac{1}{2}\int cos(2x-\frac{\pi}{8})d(2x)=\\=\frac{1}{2}\int cos(2x-\frac{\pi}{8})d(2x-\frac{\pi}{8})=\frac{1}{2}sin(2x-\frac{\pi}{8})+C$

$\int xsinxdx\\u=x=\ \textgreater \ du=dx\\dv=sinxdx=\ \textgreater \ v=-cosx\\\int xsinxdx=-xcosx-\int-cosxdx=-xcosx+sinx+C$