Question

Integral of sin^4 (6x) dx

Answer 1

Hello,


`\boxed{sin^4\ x= (3)/(8)- (cos\ 2x)/(2)+(sin\ 4x)/(8) }\\ Let's assume t=6x \ dt=6\ dx\\ \int\limits {sin^4\ 6x} \, dx = (1)/(6) *\int\limits {sin^4\ t} \, dt \\ = (1)/(6) *( (3t)/(8) - (sin\ 2t)/(4) +(sin\ 4t)/(32))+C\\ = (3x)/(8) - (sin\ 12x)/(24) +(sin\ 24x)/(192) +C`

Answer 2

The question is asking to calculate and find the integral of sin^4(6x)dx, and base on my further computation and formulation about the said equation, I would say that the integral value of the said equation is | | = 1/192 (72 x-8 sin(12 x)+sin(24 x))+constant. I hope you are satisfied with my answer and feel free to ask for more