Evaluate the following definite Integral: ∫ e^(2x)(1/x - 1/2x^2)dx, x ∈ [1, 2]

Question

Evaluate the following definite Integral:

\(\int\limits_1^2 \)e^2x\(\Big(\cfrac{1}{\text x}-\cfrac{1}{2\text x^2}\Big)\)dx

Answer 1

Let 2x = t then 2dx = dt

When x = 1 t = 2 And when x = ,t = 4

We can observe here that

Derivative of \(\cfrac{1}{\text x}=-\cfrac{1}{\text x^2}\)

Now it is in the form e^x(function + derivative of function)

So, the integral will be e^x(function)