= ∫sin^(n- 1)(x) * sinx dx

=-∫ sin (n- 1) (x) d (cosx), partial integration.

=-cosx * sin (n-1) (x)+∫ cosxd [sin (n-1) (x)], partial integral.

=-cosx * sin^(n- 1)(x)+∫cosx *(n- 1)* sin^(n-2)(x)* cosx dx

=-cosx * sin^(n- 1)(x)+(n- 1)∫sin^(n-2)(x)*( 1-sin？ x) dx

=-cosx * sin^(n- 1)(x)+(n- 1)∫sin^(n-2)(x)dx-(n- 1)j

[ 1+(n- 1)]j =-cosx * sin^(n- 1)(x)+(n- 1)∫sin^(n-2)(x)dx

j =-( 1/n)cosx * sin^(n- 1)(x)+[(n- 1)/n]∫sin^(n-2)(x)+c