Integrate: 2xe^(x^2) AND sinx/(2+cosx) If anyone could help me with these two integrals it would be greatly appreciated, thank you !
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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, $\displaystyle \int f'(x)f(x)\,dx=\frac{f(x)^2}{2}+C(onstant)$ For the second one, $\displaystyle \int\frac{f'(x)}{f(x)}dx=\ln|f(x)|+C(onstant)$ Tonio
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 ! ..
$\displaystyle \int 2xe^{x^2}dx=\int e^{x^2}dx^2=e^{x^2}+C$. similarly for the second one.
In other words, for the first one use the substitution $\displaystyle u= x^2$ and for the second, u= 2+ cos(x).
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