What is the integral of $\int {cos}^{2} (x) {tan}^{3} (x) d x$ $int cos^2(x) tan^3(x) dx$ ?

Question

1373 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-04T05:47:19

$(\frac{{(tan x)}^{2}}{2}) + c$ $((tanx)^2/2)+c$

$\int {(cos x)}^{2} {(tan x)}^{3} (d x)$ $int(cosx)^2(tanx)^3(dx)$

= $\int {(cos x)}^{2} \times \frac{{(sin x)}^{3}}{{(cos x)}^{3}} \times (d x)$ $int(cosx)^2times(sinx)^3/(cosx)^3times(dx)$

= $\int \frac{{(sin x)}^{3}}{cos x} (d x)$ $int(sinx)^3/(cosx)(dx)$

= $\int (tan x) {(sec x)}^{2} (d x)$ $int(tanx)(secx)^2(dx)$

Let $tan x = t$ $tanx = t$
$:.sec^2x dx = dt$

Replacing,
= $inttdt$

= $t^2/2+c$

Replacing back,
= $((tanx)^2/2)+c$

What is the integral of int cos^2(x) tan^3(x) dx∫cos2(x)tan3(x)dxint cos^2(x) tan^3(x) dx?