Question

（x＋5）/（x²-6x+13）的不定积分

Answer 1

∫(x+5)/（x^2-6x+13) dx
=(1/2)∫(2x-6)/（x^2-6x+13) dx +8∫dx/(x^2-6x+13)
=(1/2)ln|x^2-6x+13| +2∫dx/{ (x-3)/2]^2+1}
=(1/2)ln|x^2-6x+13| +4∫d[(x-3)/2]/{ (x-3)/2]^2+1}
=(1/2)ln|x^2-6x+13| +4arctan[(x-3)/2] +C

Answer 2

∫x+5/x²-6x+13 dx
=∫（x-3+8）/（x²-6x+13） dx
=∫(x-3)/(x²-6x+13)dx+8∫1/[(x-3)²+2²]dx
=1/2ln(x²-6x+13)+8/2 arctan(x-3)/2+c
=1/2ln(x²-6x+13)+4 arctan(x-3)/2+c

Answer 3

解：∫(x+5)/(x²-6x+13)dx=∫(x-3+8)/(x²-6x+13)dx=∫(x-3)/(x²-6x+13)dx+8∫1/[(x-3)²+4]dx=0.5ln|x²-6x+13|+2∫1/[(x-3)²/4+1]dx=0.5ln|x²-6x+13|+4arctan[0.5(x-3)]+c(c为任意常数)

希望对你有帮助

Answer 4

∫(X+5)/(X²-6X+13)dX
=∫(X-3+8)/(X²-6X+13)dX
=∫(X-3)/(X²-6X+13)dX+∫8/(X²-6X+13)dX
=(1/2)∫(2X-6)/(X²-6X+13)dX+∫8/(X²-6X+13)dX
=(1/2)∫[d(X²-6X+13)]/(X²-6X+13)+
8∫[d(X-3)]/[(X-3)²+2²]
=(1/2)㏑(X²-6X+13)+4arctan[(X-3)/2]+C