Evaluate the integral.

{eq}\displaystyle \int \arctan 8t \, \mathrm{d}t {/eq}

Question:

Evaluate the integral.

{eq}\displaystyle \int \arctan 8t \, \mathrm{d}t {/eq}

Integration by Parts:

In this question the integrand is an inverse trigonometric function. To solve the integral we will use integration by parts. We will also use substitution to evaluate this integral. In integration by parts we change the function as product of two functions and proceed accordingly.

Answer and Explanation: 1

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{eq}I=\int \tan^{-1}8x dx\\ 8x=t\\ I=\frac{1}{8}\int \tan^{-1}tdt\\ \text{Applying integration by parts}\\ I=\frac{1}{8}\left (t \tan^{-1}t-\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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