Exercise
$\int\frac{\cos\left(x\right)}{e^{3x}}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int(cos(x)/(e^(3x)))dx. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. We can solve the integral \int e^{-3x}\cos\left(x\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.
Find the integral int(cos(x)/(e^(3x)))dx
Final answer to the exercise
$-\frac{3}{8}e^{-3x}\cos\left(x\right)+\frac{1}{8}e^{-3x}\sin\left(x\right)+C_0$