Evaluate the indefinite integral.

{eq}\displaystyle \int \sec^2 \theta \tan^3 \theta\ d \theta {/eq}.

Question:

Evaluate the indefinite integral.

{eq}\displaystyle \int \sec^2 \theta \tan^3 \theta\ d \theta {/eq}.

Integrals:

We have an indefinite integral and we will use the substitution method to evaluate it. We will get a constant of integration which represents the family of antiderivatives that results to the same function when differentiated. To solve the given integral, we will use the power rule of differentiation:

$$\int x^n \text{ d}x=\frac{x^{n+1}}{n+1}+c $$

Answer and Explanation: 1

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Given:

$$\displaystyle \int \sec^2 \theta \tan^3 \theta\ \text{ d} \theta $$

We will apply the following substitution:

$$\begin{align} \tan...

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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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