Math Questions and Answers

Start Your Free Trial

Evaluate the indefinite integral.   integrate of ln(x^2+10x+24)dx

Expert Answers info

Luca B. eNotes educator | Certified Educator

calendarEducator since 2011

write5,348 answers

starTop subjects are Math, Science, and Business

You need to use integration by parts such that:

`int udv = uv - int vdu`

Considering `u = ln(x^2+10x+24)`  and `dv = dx`  yields:

`u = ln(x^2+10x+24) => du = (2x+10)/(x^2+10x+24) dx`

`dv = dx => v = x`

`int ln(x^2+10x+24)dx = xln(x^2+10x+24) - int (2x^2 + 10x)/(x^2+10x+24) dx`

Using reminder theorem yields:

`(2x^2 + 10x) = 2(x^2+10x+24) - 10x`

`(2x^2 + 10x)/(x^2+10x+24) = 2 - 10x/(x^2+10x+24)`

Integrating both sides yields:

`int (2x^2 + 10x)/(x^2+10x+24) dx= int2 dx- int 10x/(x^2+10x+24) dx`

`int (2x^2 + 10x)/(x^2+10x+24) dx = 2x - 10 int x/(x^2+10x+24) dx`

You need to come up with the substitution...

(The entire section contains 333 words.)

Unlock This Answer Now


check Approved by eNotes Editorial