Solved example of trigonometric integrals
Apply the formula: $\int\sin\left(\theta \right)^ndx$$=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)}{n}+\frac{n-1}{n}\int\sin\left(\theta \right)^{\left(n-2\right)}dx$, where $n=4$
Rewrite the trigonometric expression $\sin\left(x\right)^{2}$ inside the integral
Take the constant $\frac{1}{2}$ out of the integral
Simplify the expression inside the integral
Solve the product $\frac{3}{8}\left(\int1dx+\int-\cos\left(2x\right)dx\right)$
The integral of a constant is equal to the constant times the integral's variable
The integral of a function times a constant ($-1$) is equal to the constant times the integral of the function
Apply the formula: $\int\cos\left(ax\right)dx$$=\frac{1}{a}\sin\left(ax\right)+C$, where $a=2$
Simplify the expression inside the integral
The integral $\frac{3}{4}\int\sin\left(x\right)^{2}dx$ results in: $\frac{3}{8}x-\frac{3}{16}\sin\left(2x\right)$
Gather the results of all integrals
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
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