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

Integrate e^(-1x*3)sin(5x)

Answer

$-\frac{1}{5}e^{-3x}\cos\left(5x\right)-\frac{3}{5}\left(76.8\int2e^{-3x}\left(\cos\left(-\frac{1}{3276}x\right)+\cos\left(\frac{1}{1092}x\right)\right)\left(\cos\left(-\frac{1}{819}x\right)+\cos\left(\frac{1}{273}x\right)\right)\left(\cos\left(-\frac{1}{205}x\right)+\cos\left(\frac{4}{273}x\right)\right)\left(\cos\left(-\frac{5}{256}x\right)+\cos\left(\frac{15}{256}x\right)\right)\left(\cos\left(-\frac{5}{64}x\right)+\cos\left(\frac{15}{64}x\right)\right)\left(\cos\left(-\frac{5}{16}x\right)+\cos\left(\frac{15}{16}x\right)\right)\left(\cos\left(-\frac{5}{4}x\right)+\cos\left(\frac{15}{4}x\right)\right)\sin\left(\frac{1}{13107}x\right)\left(\cos\left(-\frac{1}{13107}x\right)+\cos\left(\frac{1}{4369}x\right)\right)dx+\frac{1}{5}e^{-3x}\sin\left(5x\right)\right)$

Step-by-step explanation

Problem

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

Multiply $3$ times $-1$

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

Unlock this step-by-step solution!

Answer

$-\frac{1}{5}e^{-3x}\cos\left(5x\right)-\frac{3}{5}\left(76.8\int2e^{-3x}\left(\cos\left(-\frac{1}{3276}x\right)+\cos\left(\frac{1}{1092}x\right)\right)\left(\cos\left(-\frac{1}{819}x\right)+\cos\left(\frac{1}{273}x\right)\right)\left(\cos\left(-\frac{1}{205}x\right)+\cos\left(\frac{4}{273}x\right)\right)\left(\cos\left(-\frac{5}{256}x\right)+\cos\left(\frac{15}{256}x\right)\right)\left(\cos\left(-\frac{5}{64}x\right)+\cos\left(\frac{15}{64}x\right)\right)\left(\cos\left(-\frac{5}{16}x\right)+\cos\left(\frac{15}{16}x\right)\right)\left(\cos\left(-\frac{5}{4}x\right)+\cos\left(\frac{15}{4}x\right)\right)\sin\left(\frac{1}{13107}x\right)\left(\cos\left(-\frac{1}{13107}x\right)+\cos\left(\frac{1}{4369}x\right)\right)dx+\frac{1}{5}e^{-3x}\sin\left(5x\right)\right)$

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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:

4. See formulas

Time to solve it:

5.6 seconds