Asked by Mycah
Integrate (((cos^2(x)*sin(x)/(1-sin(x)))-sin(x))dx
thanks
thanks
Answers
Answered by
Bosnian
If (((cos^2(x)*sin(x)/(1-sin(x)))-sin(x)) mean:
cos ^ 2 (x) * sin (x) / [ 1 - sin(x) ] - sin (x)
then:
cos ^ 2 (x) * sin (x) / [ 1 - sin(x) ] - sin (x) =
sin (x) * { cos ^ 2 (x) / [ 1 - sin(x) ] - 1 } =
sin (x) * { [ 1 - sin ^ 2 (x) ] / [ 1 - sin(x) ] - 1 } =
sin (x) * { [ 1 + sin (x) ] * [ 1 - sin(x) ] / [ 1 - sin(x) ] - 1 } =
sin (x) * [ 1 + sin(x) - 1 ] =
sin (x) * sin (x) = sin ^ 2 (x)
cos ^ 2 (x) * sin (x) / ( 1 - sin(x) ) - sin (x) = sin ^ 2 (x)
Integrate [ cos ^ 2 (x) * sin (x) / ( 1 - sin(x) ) - sin (x) ] dx = Integrate sin ^ 2 (x) dx = x / 2 + sin (2x) / 4 + C
cos ^ 2 (x) * sin (x) / [ 1 - sin(x) ] - sin (x)
then:
cos ^ 2 (x) * sin (x) / [ 1 - sin(x) ] - sin (x) =
sin (x) * { cos ^ 2 (x) / [ 1 - sin(x) ] - 1 } =
sin (x) * { [ 1 - sin ^ 2 (x) ] / [ 1 - sin(x) ] - 1 } =
sin (x) * { [ 1 + sin (x) ] * [ 1 - sin(x) ] / [ 1 - sin(x) ] - 1 } =
sin (x) * [ 1 + sin(x) - 1 ] =
sin (x) * sin (x) = sin ^ 2 (x)
cos ^ 2 (x) * sin (x) / ( 1 - sin(x) ) - sin (x) = sin ^ 2 (x)
Integrate [ cos ^ 2 (x) * sin (x) / ( 1 - sin(x) ) - sin (x) ] dx = Integrate sin ^ 2 (x) dx = x / 2 + sin (2x) / 4 + C
Answered by
Steve
Hmmm. I get x/2 - sin(2x)/4
Answered by
Bosnian
My typo.
Integrate sin ^ 2 (x) dx = x / 2 - sin (2x) / 4 + C
Integrate sin ^ 2 (x) dx = x / 2 - sin (2x) / 4 + C