Question

Evaluate the integral sin4x cos^2 4x dx

A. cos^3 4x/3 +C

B. - cos^3 4x/3 +C

C. cos^3 4x/12 +C

D. -cos^3 4x/12 +C

Answer 1

Go on: wolframalpha dot com

When page be open in rectangle type:

integrate sin(4x) cos^2(4x) dx
and click option =

After few seconds when you see result click option: Show steps


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Answer 2

Notice that the derivative of the power cos^2 (4x) shows up as multiple, so we can just reverse the chain rule

I know that it must be something like (cos 4x)^3....

so from y ' = sin 4x (cos 4x)^2
we get y = sin 4x (cos 4x)^3 (1/3) (-1/sin 4x) (1/4)
= (-1/12) cos^3 (4x) )

which if you had used brackets correctly would have been C>