Math Questions and Answers

Start Your Free Trial

`int 10/((x - 1)(x^2 + 9)) dx` Evaluate the integral

Expert Answers info

mathace eNotes educator | Certified Educator

calendarEducator since 2015

write489 answers

starTop subject is Math

Integrated `int10/[(x-1)(x^2+9)]dx`

Solve for the variables A, B, and, C using the method of partial fractions.





Equate coefficients and solve for A, B, and C.
















The first integral matches the form`int(du)/u=ln|u|+C`



Integrate the second integral using u-substitution.

Let `u=x^2+9`





The third integral matches the form `int(dx)/(x^2+a^2)=1/atan^-1(x/a)+C`




`=int1/(x-1)dx-intx/(x^2+9)dx-int1/(x^2+9)dx `



The final answer is: 

`=ln|x-1|-1/2ln(x^2+9)-1/3tan^-1(x/3)+C `



check Approved by eNotes Editorial