To find the integral of equations or variables in the form eˣ, use the following rule.

Integrate variables in the form aˣ using the exponentials rule. Integrate 2 functions multiplied together by parts; for u, choose the function that is simpler when differentiated.

Integrate variables in the form lnx using integration by parts: ∫ u (dv/dx) dx = uv − ∫ v (du/dx) dx. Let dv/dx = 1 and u = the variable in the form lnx.

Integrate logarithmic functions using integration by parts: ∫ u (dv/dx) dx = uv − ∫ v (du/dx) dx. Let dv/dx = 1 and u = the logarithmic function.

1

Evaluate ∫ 5ˣ ⁻ ² + 4²ˣ dx.

2

Find ∫ xe²ˣ dx.

3

What is ∫ 5ln(2x + 1) dx? Use the substitution a = 2x + 1.

4

Integrate (eˣ − 2)²/e²ˣ dx.

5

Integrate ∫ 5ᵉˣ dx using the substitution u = ex.