i tried this 26 times already!

Hello, peepsqueeq1

\(\displaystyle \L\int\)sin3(17x)cos3(17x)dx\displaystyle \sin^3(17x)\cdot\cos^3(17x)\,dx

We have: \(\displaystyle \L\:\int\)sin3(17x)cos2(17x)cos(17x)dx\displaystyle \sin^3(17x)\cdot\cos^2(17x)\cdot\cos(17x)\,dx

. . . \(\displaystyle =\;\L\int\)sin3(17x)[1sin2(17x)]cos(17x)dx\displaystyle \sin^3(17x)\cdot\left[1\,-\,\sin^2(17x)\right]\cdot\cos(17x)\,dx

. . . \(\displaystyle = \;\L\int\)[sin3(17x)sin5(17x)]cos(17x)dx\displaystyle \left[\sin^3(17x)\,-\,\sin^5(17x)\right]\cdot\cos(17x)\,dx

Let u=sin(17x)        du=17cos(17x)dx        cos(17x)dx=117du\displaystyle u\:=\:\sin(17x)\;\;\Rightarrow\;\;du\:=\:17\cdot\cos(17x)\,dx\;\;\Rightarrow\;\;\cos(17x)\,dx \:=\:\frac{1}{17}\,du

Substitute: \(\displaystyle \L\:\int\)\(\displaystyle \left(u^3\,-\,u^5\right)\left(\frac{1}{17}\,du\right)\;=\;\frac{1}{17}\L\int\)(u3u5)du\displaystyle \left(u^3\,-\,u^5\right)\,du


Can you finish it now?

 
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