How do you integrate #int cos^3thetasqrt(sintheta)#?

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Answer 1 · 2017-10-19T19:36:16

#=2/3sin^(3/2)x-2/7sin^(7/2)x+C#

for #theta# read #x#

#intcos^3xsin^(1/2)xdx#

#=intcosxcos^2xsin^(1/2 )xdx#

#=intcosx(1-sin^2x)sin^(1/2)xdx#

#=intcosxsin^(1/2)x-cosxsin^(5/2)xdx#

by inspection

#=2/3sin^(3/2)x-2/7sin^(7/2)x+C#

which can be simplified as required