Solve the trigonometric integral int(4sin(9x))dx

 Exercise

$\int4\sin9xdx$

 

The integral of a function times a constant ($4$) is equal to the constant times the integral of the function

$4\int\sin\left(9x\right)dx$

 

Apply the formula: $\int\sin\left(ax\right)dx$$=-\left(\frac{1}{a}\right)\cos\left(ax\right)+C$, where $a=9$

$-4\cdot \left(\frac{1}{9}\right)\cos\left(9x\right)$

 

Multiply the fraction and term in $-4\cdot \left(\frac{1}{9}\right)\cos\left(9x\right)$

$-\frac{4}{9}\cos\left(9x\right)$

 

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$-\frac{4}{9}\cos\left(9x\right)+C_0$

$-\frac{4}{9}\cos\left(9x\right)+C_0$

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