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kaiz122
 3 years ago
integrate(cos^3 x)/sin(x) dx
kaiz122
 3 years ago
integrate(cos^3 x)/sin(x) dx

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SuckMyEsophagus
 3 years ago
Best ResponseYou've already chosen the best response.0Let u = cos x du = sin x dx then, "integral [u^3 du]" or " integral [u^3 du] " = (u^4)/4 + C = (cos^4 x)/4 + C

kaiz122
 3 years ago
Best ResponseYou've already chosen the best response.0i have a question, sin x is in the denominator, how does it become the du then?

SuckMyEsophagus
 3 years ago
Best ResponseYou've already chosen the best response.0Because everything is substituted and then flipped :)

kaiz122
 3 years ago
Best ResponseYou've already chosen the best response.0i tried checking it by differentiation, then i got (cos^3x )(sinx)

SuckMyEsophagus
 3 years ago
Best ResponseYou've already chosen the best response.0Are you using your calculator?

SuckMyEsophagus
 3 years ago
Best ResponseYou've already chosen the best response.0You can integrate this directly, just notice that differentiating cos^4(x) gives you 4cos^3(x)sin(x) by the chain rule. Hence the integral of cos^3(x)sin(x) is 1/4 cos^4(x)

kaiz122
 3 years ago
Best ResponseYou've already chosen the best response.0i still don't get it, how does sin x in the denominator becomes du? dx/sinx is not equal to sinx dx right.

SuckMyEsophagus
 3 years ago
Best ResponseYou've already chosen the best response.0No their not the equal

kaiz122
 3 years ago
Best ResponseYou've already chosen the best response.0@saifoo.khan can you please help me here

AravindG
 3 years ago
Best ResponseYou've already chosen the best response.0use @AravindG if u have any integration qns in future
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