Question

Marque a alternativa que corresponde à integral indefinida de f(x) = e^(2x).

Answer 1

Olá Walisson!

A integral em questão sai por "substituição simples". Tomemos $2x = k$, então:

$\\ \mathsf{2x = k} \\\\ \mathsf{2 \ dx = dk} \\\\ \mathsf{dx = \frac{dk}{2}}$
 
 Com efeito,

$\\ \mathsf{\int e^{2x} \ dx =} \\\\\\ \mathsf{\int e^k \cdot \frac{dk}{2} =} \\\\\\ \mathsf{\frac{1}{2} \cdot \int e^k \ dk =} \\\\\\ \mathsf{\frac{1}{2} \cdot \left [ e^k \right ] =} \\\\\\ \mathsf{\frac{1}{2} \cdot \left [ e^{2x} \right ] =} \\\\\\ \boxed{\mathsf{\frac{e^{2x}}{2} + c}}$