Calculus • Step-by-Step

Integral of e^(2x) dx with Steps

Find the integral of e^(2x) step-by-step using u-substitution. Shows letting u = 2x to reach (1/2)e^(2x) + C.

Problem Statement

\int e^{2x} \, dx

Final Result

F(x) = \frac{e^{2 \cdot x}}{2} + C

Formula Required: Exponential Substitution

Dividing by the constant k accounts for the chain rule in reverse.

\int e^{kx} \, dx = \frac{1}{k}e^{kx} + C

2 Steps

Set up the indefinite integral with respect to variable $x$.

\int \left( e^{2 \cdot x} \right) \, dx

Apply the Exponential Integration to find the antiderivative.

F(x) = \frac{e^{2 \cdot x}}{2}

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

Let u = 2x, so du = 2 dx and dx = du/2. ∫ e^u (du/2) = (1/2)e^u + C = (1/2)e^(2x) + C.