# Use the substitution x = \frac{6}{5} \tan t to transform the integral I = \int \frac{dx}{\sqrt...

## Question:

Use the substitution {eq}x = \frac{6}{5} \tan t {/eq} to transform the integral {eq}I = \int \frac{dx}{\sqrt {25x^2 + 36}} {/eq} into a trigonometric integral.

{eq}I = \int {/eq} _____ dt

## Evaluation of Integral:

Integration is reverse of differentiation.It is also called anti derivative.

Here, we are going to use substitution method to evaluate the integral.

Add constant c at the end of evaluation.

## Answer and Explanation: 1

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Given integral is

{eq}\displaystyle I = \int \frac{dx}{\sqrt {25x^2 + 36}} {/eq}

Substitute, {eq}\displaystyle x = \frac{6}{5} \tan t {/eq} on...

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