Here, we show you a step-by-step solved example of trigonometric integrals. This solution was automatically generated by our smart calculator:
Apply the formula: $\int\sin\left(\theta \right)^ndx$$=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)}{n}+\frac{n-1}{n}\int\sin\left(\theta \right)^{\left(n-2\right)}dx$, where $n=4$
Multiply the single term $\frac{3}{4}$ by each term of the polynomial $\left(\frac{1}{2}x-\frac{1}{4}\sin\left(2x\right)\right)$
Apply the formula: $\int\sin\left(\theta \right)^2dx$$=\frac{1}{2}\theta -\frac{1}{4}\sin\left(2\theta \right)+C$
The integral $\frac{3}{4}\int\sin\left(x\right)^{2}dx$ results in: $\frac{1}{2}\cdot \frac{3}{4}x-\frac{1}{4}\cdot \frac{3}{4}\sin\left(2x\right)$
Gather the results of all integrals
Multiplying fractions $-\frac{1}{4} \times \frac{3}{4}$
Multiplying fractions $\frac{1}{2} \times \frac{3}{4}$
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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