Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(20tan(x)^6)dx. The integral of a function times a constant (20) is equal to the constant times the integral of the function. Applying a reduction formula for the integral of the tangent function: \displaystyle\int\tan(x)^{n}dx=\frac{1}{n-1}\tan(x)^{n-1}-\int\tan(x)^{n-2}dx. Multiplying polynomials 20 and \frac{1}{6-1}\tan\left(x\right)^{5}-\int\tan\left(x\right)^{4}dx. The integral -20\int\tan\left(x\right)^{4}dx results in: -\frac{20}{3}\tan\left(x\right)^{3}+20\left(-x+\tan\left(x\right)\right).

Solve the trigonometric integral int(20tan(x)^6)dx