Evaluate the following integrals: ∫ e^2x ((2x - 1)/(4x^2)) dx

Question

Evaluate the following integrals:

\(\int e^{2x}\left(\frac{2x - 1}{4x^2}\right)dx\)

∫ e^2x ((2x - 1)/(4x²)) dx

Answer 1

 \(\int e^{2x}\left(\frac{2x - 1}{4x^2}\right)dx\)

∫ e^2x ((2x - 1)/(4x²)) dx

Tip – If f₁(x) and f₂(x) are two functions , then an integral of the form ∫ f₁(x)f₂(x)dx can be INTEGRATED BY PARTS as

where f₁(x) and f₂(x) are the first and second functions respectively.

Taking f₁(x) = 1/2x and f₂(x) = e^2x in the first integral and keeping the second integral intact,

where c is the integrating constant.