If $\int e^x(2\sin^3x+3\sin2x)\sin x dx=e^x\cdot(\phi(x))+c$ then which of the following is false?
- A) $\phi(\frac{\pi}2)=2$
- B) $\phi(\pi)=0$
- C) $\phi(\frac{\pi}6)=\frac12$
- D) $\phi(0)=0$
I tried rearranging it so that I could put $\sin x$ or $\cos x$ as $t$, but couldn't reach anywhere.
I tried separating the two integrals and then integrating by parts, that didn't work either.
I tried to make it in the form $\int e^x(f(x)+f'(x))dx$ but in vain.
By looking at the options, it appears $\phi(x)$ could be $\sin x$ then options $B, C, D$ would satisfy but $A$ wouldn't. I am not sure though.