Integrate the following indefinite integral:

Question

(sin7x)^12 * (cos7x)^3

Hint: sin^2 + cos^2 = 1

Answer 1

= int [(sin7x)^12 * (cos7x)^2 * cos7x *dx]
= int [(sin7x)^12 * (1-sin 7x)^2 * cos7x *dx]
=int [(sin7x)^12 * cos 7x * dx] - int [(sin7x)^12 * (sin 7x)^2 * cos7x *dx]
=int[u^12*(1/7)*du] - int[u^14*(1/7)*du]
=(1/7)*(1/13)*u^13 - (1/7)*(1/15)*u^15 + C
=(1/7)*u^13*( (1/13) - (1/15)*u^2 ) + C
=(1/7)*(sin 7x)^13 * ( (1/13) - (1/15)*(sin7x)^2 ) + C

Answer 2

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