Exercise
$\int_1^2\left(\left(x+1\right)e^{-2x}\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function (x+1)e^(-2x) from 1 to 2. We can solve the integral \int\left(x+1\right)e^{-2x}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v. Solve the integral to find v.
Integrate the function (x+1)e^(-2x) from 1 to 2
Final answer to the exercise
$\frac{3}{-2}\cdot e^{-4}+e^{-2}+\frac{1}{4}\cdot e^{-2}+\frac{1}{-4}\cdot e^{-4}$