# Find the indefinite integral: {eq}\int \tan^3(7x) dx {/eq}

## Question:

Find the indefinite integral: {eq}\int \tan^3(7x) dx {/eq}

## Integration by Substitution:

The substitution for some function frequently referred to as u-substitution or substitution of variables, is a measure for determining integrals and antiderivatives that can be solved quickly. We substitute {eq}t=f(x)\\ \Rightarrow dt=f'(x) \ dx{/eq} which may help to integrate the functions with much ease and in lesser time.

## Answer and Explanation: 1

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{eq}\begin{align} \int \tan^3(7x) dx &=\int \tan^2(7x) \ \tan(7x) \ dx\\ &=\int (\sec^2(7x) -1) \ \tan(7x) \ dx\\ &=\int (\sec^2(7x) \ \tan(7x) - \...

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