Exercise
$\int\:e^{\frac{x}{2}}\cdot\:cos\left(3x\right)dx$
Step-by-step Solution
Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(e^(x/2)cos(3x))dx. We can solve the integral \int e^{\frac{x}{2}}\cos\left(3x\right)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.
Find the integral int(e^(x/2)cos(3x))dx
Final answer to the exercise
$\frac{2}{37}e^{\frac{x}{2}}\cos\left(3x\right)+\frac{12}{37}e^{\frac{x}{2}}\sin\left(3x\right)+C_0$