How do you use Integration by Substitution to find $\int tan (x) \cdot {sec}^{3} (x) d x$ $inttan(x)*sec^3(x)dx$ ?

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How do you use Integration by Substitution to find $\int tan (x) \cdot {sec}^{3} (x) d x$ $inttan(x)*sec^3(x)dx$ ?

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Answer 1 · 2014-08-04T21:33:43

$= \frac{{sec}^{3} (x)}{3} + c$ $=(sec^3(x))/3+c$ , where $c$ $c$ is a constant

Explanation

$= \int tan (x) \cdot {sec}^{3} (x) d x$ $=inttan(x)*sec^3(x)dx$

let's have $sec x = t$ $secx=t$

$sec (x) \cdot tan (x) d x = d t$ $sec(x)*tan(x)dx=dt$

$= \int (tan (x) sec (x)) \cdot {sec}^{2} (x) d x$ $=int(tan(x)sec(x))*sec^2(x)dx$

$= \int t^{2} d t$ $=intt^2dt$ , which is quite straight forward,

$= \frac{t^{3}}{3} + c$ $=t^3/3+c$ , where $c$ $c$ is a constant

$= \frac{{sec}^{3} (x)}{3} + c$ $=(sec^3(x))/3+c$ , where $c$ $c$ is a constant

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How do you use Integration by Substitution to find $\int tan (x) \cdot {sec}^{3} (x) d x$ $inttan(x)*sec^3(x)dx$ ?

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How do you use Integration by Substitution to find $\int tan (x) \cdot {sec}^{3} (x) d x$ $inttan(x)*sec^3(x)dx$ ?