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Rewrite the integrand $\left(x+\sin\left(x\right)\right)^2$ in expanded form
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$\int\left(x^2+2x\sin\left(x\right)+\sin\left(x\right)^2\right)dx$
Learn how to solve problems step by step online. Solve the trigonometric integral int((x+sin(x))^2)dx. Rewrite the integrand \left(x+\sin\left(x\right)\right)^2 in expanded form. Expand the integral \int\left(x^2+2x\sin\left(x\right)+\sin\left(x\right)^2\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^2dx results in: \frac{x^{3}}{3}. The integral \int2x\sin\left(x\right)dx results in: -2x\cos\left(x\right)+2\sin\left(x\right).