考研确定高数积分需要详细步骤吗？

∫(0,π)x(sinx)^9dx=π/2 ∫(0,π)(sinx)^9dx

=π ∫(0,π/2)(sinx)^9dx

=π 8!！/9!！

∫(π/2,π)x(sinx)^9dx

=∫(0,π/2)(x+π/2)(sin(x+π/2))^9dx

=-∫(0,π/2)(x+π/2)(cosx)^9dx

=-∫(0,π/2)x(cosx)^9 dx -π/2∫(0,π/2)(cosx)^9dx

=∫(π/2,0)(π/2-x)(sinx)^9dx-π/2∫(0,π/2)(cosx)^9dx

=-∫(0,π/2)(π/2-x)(sinx)^9 dx -π/2∫(0,π/2)(cosx)^9dx

=-∫(0，π/2)π/2 (sinx)^9 dx +∫(0，π/2)x(sinx)^9 dx -π/2∫(0,π/2)(cosx)^9dx

=-π/2∫(0,π/2)(sinx)^9 dx -π/2∫(0,π/2)(cosx)^9 dx+∫(0，π/2) x(sinx)^9 dx

=-π/2 ( 2* 8!！/9!！)+∫(0，π/2) x(sinx)^9 dx

∫(0,π/2)x(sinx)^9dx = ∫(0,π)x(sinx)^9dx-∫(π/2,π)x(sinx)^9dx

=π 8!！/9!！-[-π/2 ( 2* 8!！/9!！)+∫(0，π/2) x(sinx)^9 dx]

=2π 8!！/9!！-∫(0，π/2) x(sinx)^9 dx

∫(0，π/2) x(sinx)^9 dx=π 8！！/9!！