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sha0403
Group Title
help me to integrate this.. integration of cos^3 x dx..
 one year ago
 one year ago
sha0403 Group Title
help me to integrate this.. integration of cos^3 x dx..
 one year ago
 one year ago

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Asad0000 Group TitleBest ResponseYou've already chosen the best response.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.
 one year ago

sha0403 Group TitleBest ResponseYou've already chosen the best response.0
but i still did not get sin x  1/3 sin^3 (x)+c... bcoz the question ask to prove..
 one year ago

Asad0000 Group TitleBest ResponseYou've already chosen the best response.1
Look. When you did the substitutions as I told you above, you should end up with the following integral:\[\int\limits_{}^{} [(1  \sin^{2}(x) )\cos(x) ]dx\]
 one year ago

RadEn Group TitleBest ResponseYou've already chosen the best response.0
int (1sin^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
 one year ago

sha0403 Group TitleBest ResponseYou've already chosen the best response.0
ok the i get integration of (cos x  u^2) du.. how to solve integration of cos x in term of u?
 one year ago

Asad0000 Group TitleBest ResponseYou've already chosen the best response.1
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.
 one year ago

Eng.Mido Group TitleBest ResponseYou've already chosen the best response.1
\[\int\limits(\cos ^{3}{x})=\int\limits(cosx*\cos^{2}{x})=\int\limits(cosx(1\sin ^{2}{x})=\int\limits(cosx)(sinx)^2(cosx)=sinx1/3(\sin ^{3}{x})+\]
 one year ago

Eng.Mido Group TitleBest ResponseYou've already chosen the best response.1
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 1sin^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
 one year ago

sha0403 Group TitleBest ResponseYou've already chosen the best response.0
but how to solve the integration of cos xu^2 du?
 one year ago

Eng.Mido Group TitleBest ResponseYou've already chosen the best response.1
\[\cos(xu^2) du\]
 one year ago

Eng.Mido Group TitleBest ResponseYou've already chosen the best response.1
is this ur question ?
 one year ago

sha0403 Group TitleBest ResponseYou've already chosen the best response.0
no.. like this integration of (cos x)(u^2) du
 one year ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.0
@sha0403\[\Large \int\limits (1 \sin^2 x)(\cos x dx)\]let \(u=\sin x\), \(du = \cos x dx\)
 one year ago

sha0403 Group TitleBest ResponseYou've already chosen the best response.0
yes but how ti integrate cos x in term of du?
 one year ago

Eng.Mido Group TitleBest ResponseYou've already chosen the best response.1
use the substitution method.
 one year ago

sha0403 Group TitleBest ResponseYou've already chosen the best response.0
ok i get it now.. thank u..sorry i was too slow..
 one year ago

Eng.Mido Group TitleBest ResponseYou've already chosen the best response.1
\[\cos^2x*cosx dx=\cos^3x \]
 one year ago

Eng.Mido Group TitleBest ResponseYou've already chosen the best response.1
U r wlcme :) ... np!
 one year ago
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