Math Help - integration

1. integration

Integrate:

2xe^(x^2)

AND

sinx/(2+cosx)

If anyone could help me with these two integrals it would be greatly appreciated, thank you !

2. Originally Posted by christina
Integrate:

2xe^(x^2)

AND

sinx/(2+cosx)

If anyone could help me with these two integrals it would be greatly appreciated, thank you !

Hints: for the first one, $\int f'(x)f(x)\,dx=\frac{f(x)^2}{2}+C(onstant)$

For the second one, $\int\frac{f'(x)}{f(x)}dx=\ln|f(x)|+C(onstant)$

Tonio

3. Originally Posted by christina
Integrate:

2xe^(x^2) Mr F says: Substitute u = x^2.

AND

sinx/(2+cosx) Mr F says: Substitute u = 2 + cos x.

If anyone could help me with these two integrals it would be greatly appreciated, thank you !
..

4. $\int 2xe^{x^2}dx=\int e^{x^2}dx^2=e^{x^2}+C$.
similarly for the second one.

5. In other words, for the first one use the substitution $u= x^2$ and for the second, u= 2+ cos(x).