Find \(\int 2x(x^2+5)^4\,dx\).

Find \(\int 3(3x+1)^7\,dx\).

Evaluate \(\int_0^1 2x e^{x^2}\,dx\).

Find \(\int \frac{2x}{x^2+9}\,dx\).

Find \(\int \cos(5x)\,dx\).

Find \(\int x\sqrt{x^2+4}\,dx\).

Evaluate \(\int_1^2 \frac{1}{2x+1}\,dx\).

Find \(\int \frac{x}{\sqrt{1-x^2}}\,dx\).

Evaluate \(\int_0^\pi \sin x\,(1+\cos x)^3\,dx\).

Find \(\int \tan x\,dx\) by writing \(\tan x=\frac{\sin x}{\cos x}\).