I hate it. Stuck on 2 integration problems
a). $\displaystyle \int\frac{1}{\sqrt{x}}\sin\sqrt{x}\ .dx\ where\ x = u^2$
b). $\displaystyle \int\frac{2}{e^{2x} + 4}\ where\ u = e^{2x} + 4$
Thanks for any help
In that case then, if $\displaystyle u=e^{2x}+4$, then $\displaystyle \,du=2e^{2x}\,dx$
Thus, the integral becomes $\displaystyle \int\frac{2\,dx}{u}=\int\frac{2e^{2x}\,dx}{e^{2x}u }$
Since $\displaystyle u=e^{2x}+4$, that means that $\displaystyle e^{2x}=u-4$
So the integral becomes $\displaystyle \int\frac{\,du}{u\left(u-4\right)}$
And now, you'll need to apply the technique of partial fractions.