Final answer to the problem
Step-by-step Solution
Specify the solving method
Applying a reduction formula for the integral of the tangent function: $\displaystyle\int\tan(x)^{n}dx=\frac{1}{n-1}\tan(x)^{n-1}-\int\tan(x)^{n-2}dx$
Learn how to solve problems step by step online.
$\frac{1}{5-1}\tan\left(x\right)^{4}-\int\tan\left(x\right)^{3}dx$
Learn how to solve problems step by step online. Solve the trigonometric integral int(tan(x)^5)dx. 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. Simplify the expression inside the integral. The integral -\int\tan\left(x\right)^{3}dx results in: -\frac{1}{2}\sec\left(x\right)^2-\ln\left(\cos\left(x\right)\right). Gather the results of all integrals.