Question

Help please!integrate the following:B3%7D%20%28x%29%20dx" id="TexFormula1" title=" \displaystyle \int \cos ^{3} (x) dx" alt=" \displaystyle \int \cos ^{3} (x) dx" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

i think its help..............

Answer 2

Answer:

$\displaystyle \sin (x) - \frac{ { \sin}^{3} (x)}{3} + \rm C$

Step-by-step explanation:

we would like to integrate the following integration

$\displaystyle \int \cos ^{3} (x) dx$

in order to do so rewrite

$\displaystyle \int \cos ^{2} (x) \cos(x) dx$

we can also rewrite cos²(x) by using trigonometric indentity

$\displaystyle \int( 1 - \sin ^{2} (x) )\cos(x) dx$

to apply u-substitution we'll choose

$\rm \displaystyle u = \sin ^{} (x) \quad \text{and} \quad du = \cos(x) dx$

thus substitute:

$\displaystyle \int( 1 - {u}^{2} )du$

apply substraction integration and:

$\displaystyle \int 1du - \int {u}^{2} du$

use constant integration rule:

$\displaystyle u - \int {u}^{2} du$

use exponent integration rule:

$\displaystyle u - \frac{ {u}^{3} }{3}$

back-substitute:

$\displaystyle \sin (x) - \frac{ { \sin}^{3} (x)}{3}$

finally we of course have to add constant of integration:

$\displaystyle \sin (x) - \frac{ { \sin}^{3} (x)}{3} + \rm C$