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hi, can anyone explain me how to get the integral:
∫((sin^3 x)/sqrt(cos x))dx
 one year ago
 one year ago
hi, can anyone explain me how to get the integral: ∫((sin^3 x)/sqrt(cos x))dx
 one year ago
 one year ago

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ekaknrBest ResponseYou've already chosen the best response.0
well, you will need to take cos x as a variable, say 't', and then use chain rule to say that dx = dt/sinx Then, you substitute for cos x and simplify and then integrate, and finally substitute for 't' to get the answer.
 one year ago

yegielBest ResponseYou've already chosen the best response.0
thanks a lot for your reply, but can you explain a little bit more de chain rule part?
 one year ago

rbliss11Best ResponseYou've already chosen the best response.0
You first need to change sin^3x as follows: sin^3x =sin^2x sinx =(1cos^2x)sinx Substitute this form into original integral and distribute cos^(1/2) over (1cos^2x) so you now have integral of (cos^(1/2)xsin x  cos^(3/2)xsinx )dx Now you can make the t substitution described earlier and you will have integral of t^(1/2) t^(3/2) dt which can be integrated by power rule.
 10 months ago
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