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Step-by-step Solution

Trigonometric integral int(-1*cos(3*x)+7*sin(4*x))dx

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Answer

$-\frac{1}{3}\sin\left(3x\right)-\frac{7}{4}\cos\left(4x\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(\left(-1\right)\cdot\cos\left(3x\right)+7\sin\left(4x\right)\right)dx$
1

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int-\cos\left(3x\right)dx+\int7\sin\left(4x\right)dx$
2

Take the constant out of the integral

$-\int\cos\left(3x\right)dx+\int7\sin\left(4x\right)dx$

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Answer

$-\frac{1}{3}\sin\left(3x\right)-\frac{7}{4}\cos\left(4x\right)+C_0$
$\int\left(\left(-1\right)\cdot\cos\left(3x\right)+7\sin\left(4x\right)\right)dx$

Main topic:

Trigonometric integrals

Time to solve it:

~ 1.23 seconds