Question

help me to integrate this.. integration of cos^3 x dx..

Answer 1

split the cos^3x into cosx and cos^2x
then use the trigonometric substitution. Replace cos^2x by (1 - sin^2x). Now you can use some integrate it.

Answer 2

but i still did not get sin x - 1/3 sin^3 (x)+c... bcoz the question ask to prove..

Answer 3

Look. When you did the substitutions as I told you above, you should end up with the following integral:\[\int\limits_{}^{} [(1 - \sin^{2}(x) )\cos(x) ]dx\]

Answer 4

int (1-sin^2 x)cosx dx
= int cosx dx - int sin^2 x cosx dx
for int cosx dx = ....
and to find int sin^2 x cosx dx, use int by sub,
let u=sinx
du = ....
continue it

Answer 5

ok the i get integration of (cos x - u^2) du.. how to solve integration of cos x in term of u?

Answer 6

if u = sin(x), then du = cos(x)dx.
So replace the sin^2(x) in the original integral by u^2 and cos(x)dx by du.
You will have a really trivial integral.

Answer 7

\[\int\limits(\cos ^{3}{x})=\int\limits(cosx*\cos^{2}{x})=\int\limits(cosx(1-\sin ^{2}{x})=\int\limits(cosx)-(sinx)^2(cosx)=sinx-1/3(\sin ^{3}{x})+\]

Answer 8

a proof for my answer: cos^3x can be written as cos^2x*cosx. Then, we all know that cos^2x can be written as 1-sin^2x. then we solve the bracket. then we'll find (sinx)^2*cosx , this remind us of the integration rule where [f(x)]^n*f'(x) = ([f(x)]^n+1/n+1)+c

Answer 9

but how to solve the integration of cos x-u^2 du?

Answer 10

\[\cos(x-u^2) du\]

Answer 11

is this ur question ?

Answer 12

no.. like this integration of (cos x)-(u^2) du

Answer 13

@sha0403\[\Large \int\limits (1- \sin^2 x)(\cos x dx)\]let \(u=\sin x\), \(du = \cos x dx\)

Answer 14

yes but how ti integrate cos x in term of du?

Answer 15

use the substitution method.

Answer 16

ok i get it now.. thank u..sorry i was too slow..

Answer 17

\[\cos^2x*cosx dx=\cos^3x \]

Answer 18

U r wlcme :) ... np!