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

1. kaiz122

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2. tishara429

bhyu

3. kaiz122

what?

4. SuckMyEsophagus

Let 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

5. kaiz122

i have a question, sin x is in the denominator, how does it become the du then?

6. SuckMyEsophagus

Because everything is substituted and then flipped :)

7. kaiz122

i tried checking it by differentiation, then i got (cos^3x )(-sinx)

8. SuckMyEsophagus

9. kaiz122

no,

10. SuckMyEsophagus

You 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)

11. kaiz122

i still don't get it, how does sin x in the denominator becomes du? dx/sinx is not equal to sinx dx right.

12. SuckMyEsophagus

No their not the equal

13. kaiz122

14. saifoo.khan

@dpaInc HELP!!!!!

15. dpaInc

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16. kaiz122

thank you

17. AravindG

oh i was late :(

18. AravindG

use @AravindG if u have any integration qns in future