Evaluate the integral using subsitution rule #int cos^3xsinx dx#?

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Answer 1 · 2017-01-19T01:54:30

#intcos^(3)(x)sin(x)dx=(-cos^(4)(x))/4+C#

Let

#u=cos(x)#

then

#du=-sin(x)#

Then we can write

#intcos^(3)(x)sin(x)dx=-intu^3du=-u^(4)/4+C#

Then by substituting #cos(x)# back in we get

#ul(intcos^(3)(x)sin(x)dx=(-cos^(4)(x))/4+C)#