(1) $\int \sin ^{3} x \cos ^{2} x d x$
(2) $\int \sin ^{4} x \cos ^{2} x d x$

Step 1 ：\(u = \sin x\)

Step 2 ：\(du = \cos x dx\)

Step 3 ：\(\int \sin ^{3} x \cos ^{2} x d x = \int u^3 (1-u^2) du\)

Step 4 ：\(= \int (u^3 - u^5) du\)

Step 5 ：\(= \frac{1}{4}u^4 - \frac{1}{6}u^6 + C\)

Step 6 ：\(= \frac{1}{4}\sin^4 x - \frac{1}{6}\sin^6 x + C\)

Step 7 ：\(\boxed{\frac{1}{4}\sin^4 x - \frac{1}{6}\sin^6 x + C}\)

Step 8 ：\(\int \sin ^{4} x \cos ^{2} x d x = \int (1-\cos^2 x)^2 \cos^2 x dx\)

Step 9 ：\(v = \cos x\)

Step 10 ：\(dv = -\sin x dx\)

Step 11 ：\(\int \sin ^{4} x \cos ^{2} x d x = -\int (1-v^2)^2 v^2 dv\)

Step 12 ：\(= -\int (v^6 - 2v^4 + v^2) dv\)

Step 13 ：\(= -\frac{1}{7}v^7 + \frac{2}{5}v^5 - \frac{1}{3}v^3 + D\)

Step 14 ：\(= -\frac{1}{7}\cos^7 x + \frac{2}{5}\cos^5 x - \frac{1}{3}\cos^3 x + D\)

Step 15 ：\(\boxed{-\frac{1}{7}\cos^7 x + \frac{2}{5}\cos^5 x - \frac{1}{3}\cos^3 x + D}\)