What is the integral of $\int {tan}^{3} x sec x d x$ $int tan^3x secxdx$ ?

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What is the integral of $\int {tan}^{3} x sec x d x$ $int tan^3x secxdx$ ?

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Answer 1 · 2016-01-18T14:37:30

$\int {tan}^{3} x sec x d x = \frac{1}{3} {sec}^{3} x - sec x + C$ $int tan^3x secx dx = 1/3 sec^3x-secx +C$ . If you really want the integral of that integral ask and we'll see what we can do.

Explanation:

Useful facts:

$\frac{d}{d x} (sec x) = sec x tan x$ $d/dx(secx) = secxtanx$

${tan}^{2} x = {sec}^{2} x - 1$ $tan^2x = sec^2x-1$

$\int {tan}^{3} x sec x d x = \int ({sec}^{2} x - 1) sec x tan x d x$ $int tan^3x secx dx = int(sec^2x-1)secxtanx dx$

Let $u = sec x$ $u = secx$ , so that $d u = sec x tan x d x$ $du = secxtanxdx$ .

The integral then is $\int (u^{2} - 1) d u$ $int(u^2-1) du$ .

The student should be able to finish from here.

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What is the integral of $\int {tan}^{3} x sec x d x$ $int tan^3x secxdx$ ?

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Explanation:

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What is the integral of int tan^3x secxdx∫tan3xsecxdxint tan^3x secxdx?

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What is the integral of $\int {tan}^{3} x sec x d x$ $int tan^3x secxdx$ ?