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\int e^{\left(3\right)\left(-1\right)\cdot x}\sin\left(5x\right)dx

Integral of e^(3*-*x)sin(5*x)

Answer

$\frac{5}{8}\left(-\frac{3}{25}e^{-3x}\sin\left(5x\right)-\frac{1}{5}e^{-3x}\cos\left(5x\right)\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int e^{\left(3\right)\left(-1\right)\cdot x}\sin\left(5x\right)dx$
1

Multiply $3$ times $-1$

$\int e^{-3x}\sin\left(5x\right)dx$

Unlock this step-by-step solution!

Answer

$\frac{5}{8}\left(-\frac{3}{25}e^{-3x}\sin\left(5x\right)-\frac{1}{5}e^{-3x}\cos\left(5x\right)\right)+C_0$

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$\int e^{\left(3\right)\left(-1\right)\cdot x}\sin\left(5x\right)dx$

Main topic:

Integration by parts

Used formulas:

6. See formulas

Time to solve it:

~ 0.71 seconds