Learn how to solve problems step by step online. Solve the trigonometric integral int(-(cos(x)^6-5cos(x)^2-cos(x))sin(x))dx. The integral of a function times a constant (-1) is equal to the constant times the integral of the function. Rewrite the integrand \sin\left(x\right)\left(\cos\left(x\right)^6-5\cos\left(x\right)^2-\cos\left(x\right)\right) in expanded form. Expand the integral \int\left(\cos\left(x\right)^6\sin\left(x\right)-5\cos\left(x\right)^2\sin\left(x\right)+\frac{-\sin\left(2x\right)}{2}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral -\int\cos\left(x\right)^6\sin\left(x\right)dx results in: \frac{\cos\left(x\right)^{7}}{7}.

Solve the trigonometric integral int(-(cos(x)^6-5cos(x)^2-cos(x))sin(x))dx