Exercise
$\int\left(\frac{sin\left(-2x\right)}{e^{8x}}\right)dx$
Step-by-step Solution
Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(sin(-2x)/(e^(8x)))dx. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Use the odd-even identity \sin(-\theta)=-\sin(\theta). The integral of a function times a constant (-1) is equal to the constant times the integral of the function. We can solve the integral \int e^{-8x}\sin\left(2x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula.
Find the integral int(sin(-2x)/(e^(8x)))dx
Final answer to the exercise
$\frac{2}{17}e^{-8x}\sin\left(2x\right)+\frac{1}{34}e^{-8x}\cos\left(2x\right)+C_0$