What is the Integral of ${(tan (x))}^{4}$ $(tan(x))^4$ ?

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Answer 1 · 2017-01-13T19:36:35

${tan}^{3} x - tan x + x + C$ $tan^3x-tanx+x+C$ .

Let $I = \int {(tan x)}^{4} d x = \int {tan}^{4} x d x$ $I=int(tanx)^4dx=inttan^4xdx$ .

$:. I=inttan^2xtan^2xdx$

$=inttan^2x(sec^2x-1)dx$

$=inttan^2xsec^2xdx-inttan^2xdx$

$=J-int(sec^2x-1)dx$

$=J-intsec^2xdx+int1dx$

$=J-tanx+x$ , where,

$J=inttan^2xsec^2xdx$

To find $J," we subst. "y=tanx," so that, "dy=sec^2xdx$ .

$:. J=inty^2dy=y^3/3=1/3tan^3x$ . Finally, we have,

$I=1/3tan^3x-tanx+x+C$ .

Enjoy Maths.!

What is the Integral of (tan(x))^4(tan(x))4 (tan(x))^4?