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Step-by-step Solution

Trigonometric integral $\frac{\int3x\sin\left(x\right)dx}{\cos\left(x\right)^4}$

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Answer

$\frac{3\left(-x\cos\left(x\right)+\sin\left(x\right)\right)}{\cos\left(x\right)^4}+C_0$

Step-by-step explanation

Problem to solve:

$\frac{\int3\sin\left(x\right)\cdot xdx}{\cos\left(x\right)^4}$
1

Take the constant out of the integral

$\frac{3\int x\sin\left(x\right)dx}{\cos\left(x\right)^4}$
2

Use the integration by parts theorem to calculate the integral $\int x\sin\left(x\right)dx$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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Answer

$\frac{3\left(-x\cos\left(x\right)+\sin\left(x\right)\right)}{\cos\left(x\right)^4}+C_0$
$\frac{\int3\sin\left(x\right)\cdot xdx}{\cos\left(x\right)^4}$

Main topic:

Integration by parts

Used formulas:

4. See formulas

Time to solve it:

~ 0.75 seconds

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