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Evaluate the integral \int \frac{tan^3 (\sqrt{t})sec^2(\sqrt{t})}{\sqrt{t}}dt

Question:

Evaluate the integral {eq}\int \frac{tan^3 (\sqrt{t})sec^2(\sqrt{t})}{\sqrt{t}}dt{/eq}

Integration by Substitution:

The trigonometric tangent function given in the integrand is a composite function. The coefficient of trigonometric function is its differential coefficient. So we will substitute for this tangent function. The integrand upon substitution becomes simple and can be easily integrated.

Answer and Explanation:

We will use the following substitution:

{eq}\begin{align} \tan ( \sqrt{t} ) &=u\\ \Rightarrow \sec^2(\sqrt{t}) \frac{1}{2\sqrt{t}} \,...

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How to Solve Integrals Using Substitution

from Math 104: Calculus

Chapter 13 / Lesson 5
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