Question

求解不定积分：∫(x^5)/(Cx+D)dx,C,D 为常数.

Answer 1

求解不定积分：∫(x⁵)/(Cx+D)dx,C,D 为常数.

当c≠0时：

∫{[x⁵/(cx+d)]dx=∫[(1/c)x⁴-(d/c²)x³+(d²/c³)x²-(d³/c⁴)x+(d⁴/c⁵)]-d⁵/[c⁴(cx+d)]}dx

=(1/5c)x⁵-(d/4c²)x⁴+(d²/3c³)x³-(d³/2c⁴)x²+(d⁴/c⁵)x-(d⁵/c⁵)ln∣cx+d∣+C

当c=0时∫(x⁵/d)dx=x⁶/(6d)+C.