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Find: {eq}\int \tan^2( \frac{x}{2} ) \, \mathrm{d}x {/eq}.

Question:

Find: {eq}\int \tan^2( \frac{x}{2} ) \, \mathrm{d}x {/eq}.

Evaluate the Integral Function by U-substitution Method:

In integral calculus, to integrate a composite function, we applied the U-substitution method. Let {eq}f(x) \cdot g(x) {/eq} be a function, by this methodology, we substitute {eq}u=g(x) {/eq} and {eq}du=g'(x) {/eq} and integral as usual. In the final step, we substitute back {eq}u=g(x). {/eq}

Answer and Explanation:

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  • The given integral function is: {eq}\int \tan ^2\left(\frac{x}{2}\right) \ dx {/eq}


Let us integrate the integral function:

$$\begin{align*} \int...

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How to Solve Integrals Using Substitution

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Chapter 13 / Lesson 5
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Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples.


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