Step-by-Step Solution
Key Concept: General
Let $I = \int \sin^{10} x \cos^3 x dx = \int \sin^{10} x (1 - \sin^2 x) (\cos x dx)$<br>Put $\sin x = t \Rightarrow \cos x dx = dt$<br>$\therefore I = \int t^{10} (1 - t^2) dt = \int (t^{10} - t^{12}) dt$<br>$= \frac{t^{11}}{11} - \frac{t^{13}}{13} + C$<br>$= \frac{\sin^{11} x}{11} - \frac{\sin^{13} x}{13} + C$
Correct Answer: $\frac{\sin^{11} x}{11} - \frac{\sin^{13} x}{13} + C$