Final answer to the problem
$-\frac{1}{26}e^{-x}\cos\left(5x\right)+\frac{5}{26}e^{-x}\sin\left(5x\right)+C_0$
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We can solve the integral $\int e^{-x}\cos\left(5x\right)dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula
$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
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$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
Learn how to solve problems step by step online. int(e^(-x)cos(5x))dx. We can solve the integral \int e^{-x}\cos\left(5x\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.
Final answer to the problem
$-\frac{1}{26}e^{-x}\cos\left(5x\right)+\frac{5}{26}e^{-x}\sin\left(5x\right)+C_0$
