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


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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Indefinite Integrals as Anti Derivatives


Chapter 12 / Lesson 11

Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.

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