Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate using trigonometric identities
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
- Load more...
We identify that the integral has the form $\int\tan^m(x)\sec^n(x)dx$. If $n$ is even, then the secant function is expressed as the tangent function. The factor $\sec^n(x)$ is separated in two factors: $\sec^2(x)$ and $\left(\tan^2(x)+1\right)^{n-4}$
Learn how to solve trigonometric integrals problems step by step online.
$\int\tan\left(x\right)^3\left(\tan\left(x\right)^2+1\right)\sec\left(x\right)^2dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(tan(x)^3sec(x)^4)dx. We identify that the integral has the form \int\tan^m(x)\sec^n(x)dx. If n is even, then the secant function is expressed as the tangent function. The factor \sec^n(x) is separated in two factors: \sec^2(x) and \left(\tan^2(x)+1\right)^{n-4}. We can solve the integral \int\tan\left(x\right)^3\left(\tan\left(x\right)^2+1\right)\sec\left(x\right)^2dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \tan\left(x\right) it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation.
