Question

Найти первообразную.СРОЧНО

Answer 1

1) x^2-3x-4=0  (x-4)(x+1)=0

1/(x-4)(x+1)=1/5(x-4)-1/5(x+1)

=1/5(ln|x-4|-ln|x+1|)+C=(1/5)ln(|x-4|/|x+1|)+C

x^3/(x-1)=(x^3-1)/(x-1)+1/(x-1)=x^2+1+x+1/(x-1)

=x^3/3+x^2/2+x+ln|x-1|+C

3)2(x+3)/(x-5)(x-1)

A/(x-5)+B/(x-1)=(Ax+Bx-A+5B)/(x-5)(x-1)

A+B=1   A=1-B

5B-A=3  5B-1+B=3  B=2/3  A=1/3

1/3(x+5)+2/3(x+1)

=2/3ln|x+5|+4/3ln|x+1|+C