# Thread: Definite Integral: int[1,3][(x+1)/(x(x^2+1))]dx (I don't get correct value)

1. ## Definite Integral: int[1,3][(x+1)/(x(x^2+1))]dx (I don't get correct value)

Ok so I evaluated the indefinite integral and got the right answer but when I plugged in the bounds, I got the wrong answer.

Calculate the definite integral:

. . . . .$\displaystyle \int_1^3\, f(x)\, dx\, =\, F(x)\, =\, \int_1^3\, \dfrac{x\, +\, 1}{x\, (x^2\, +\, 1)}\, dx$

Computed by Maxima:

. . .$\displaystyle \int\, f(x)\, dx\,$

. . . . . . .$=\, \ln\left(\big|x\big|\right)\, -\, \dfrac{\ln(x^2\, +\, 1)}{2}\, +\, \arctan(x)\, +\, C$

. . .$\displaystyle \int_1^3\, f(x)\, dx\,$

. . . . . . .$=\, \ln(3)\, -\, \dfrac{\ln(10)}{2}\, +\, \arctan(3)\, +\, \dfrac{2\ln(2)\, -\, \pi}{4}$

. . . . . . .$\approx 0.7575409414518656$

For the last term I had arctan(1) which is exactly double the last term the int calculator had.

Sent from my LGLS755 using Tapatalk

2. Originally Posted by Seed5813
Ok so I evaluated the indefinite integral and got the right answer but when I plugged in the bounds, I got the wrong answer.

Calculate the definite integral:

. . . . .$\displaystyle \int_1^3\, f(x)\, dx\, =\, F(x)\, =\, \int_1^3\, \dfrac{x\, +\, 1}{x\, (x^2\, +\, 1)}\, dx$

Computed by Maxima:

. . .$\displaystyle \int\, f(x)\, dx\,$

. . . . . . .$=\, \ln\left(\big|x\big|\right)\, -\, \dfrac{\ln(x^2\, +\, 1)}{2}\, +\, \arctan(x)\, +\, C$

. . .$\displaystyle \int_1^3\, f(x)\, dx\,$

. . . . . . .$=\, \ln(3)\, -\, \dfrac{\ln(10)}{2}\, +\, \arctan(3)\, +\, \dfrac{2\ln(2)\, -\, \pi}{4}$

. . . . . . .$\approx 0.7575409414518656$

For the last term I had arctan(1) which is exactly double the last term the int calculator had.
What did you get when you rearranged your terms to match what the calculator had, and then combined the last two terms into one fraction?

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•