A calculadora encontrará a integral/antiderivada de
e2x, com as etapas mostradas.
Calculadora relacionada: Calculadora integral
Solução
Let u=2x.
Then du=(2x)′dx=2dx (steps can be seen »), and we have that dx=2du.
Thus,
∫e2xdx=∫2eudu
Apply the constant multiple rule ∫cf(u)du=c∫f(u)du with c=21 and f(u)=eu:
∫2eudu=(2∫eudu)
The integral of the exponential function is ∫eudu=eu:
2∫eudu=2eu
Recall that u=2x:
2eu=2e(2x)
Portanto,
∫e2xdx=2e2x
Adicione a constante de integração:
∫e2xdx=2e2x+C
Answer: ∫e2xdx=2e2x+C