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Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
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$\int\tan\left(x\right)^5dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int((sin(x)^5)/(cos(x)^5))dx. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. 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).