Question

Evaluate the integral. (use c for the constant of integration.) 7xe2x (1 2x)2 dx

Answer 1

To evaluate the integral ∫ 7xe^2x (1 - 2x)^2 dx, we can use integration by parts.

Step-by-step explanation:

To evaluate the integral ∫ 7xe^2x (1 - 2x)^2 dx, we can use integration by parts. Let u = 7x, dv = e^2x (1 - 2x)^2 dx. Then, we have du = 7 dx and v = ∫ e^2x (1 - 2x)^2 dx.

Using the integration by parts formula, ∫ u dv = uv - ∫ v du, we can evaluate the integral as follows:

∫ 7xe^2x (1 - 2x)^2 dx = 7x ∫ e^2x (1 - 2x)^2 dx - ∫ (∫ e^2x (1 - 2x)^2 dx) 7 dx