## sjg13e one year ago Help with a calculus problem (integration by parts)

1. sjg13e

$integrate \ln(2x+1)dx$

2. sjg13e

I have some work, give me a few minutes to input it

3. sjg13e

$\int\limits_{}^{}\ln(2x+1)dx = x*\ln(2x+1) - \int\limits_{}^{}\frac{ 2x }{ 2x +1 }$

4. sjg13e

I don't know how to take the integral of 2x / 2x + 1. I've viewed solutions online and I've seen...

5. sjg13e

6. sjg13e

I don't know why they split it into (2x - 1 + 1)/2x +1 Everything else I can do, except I just don't understand that part

7. ganeshie8

do you still remember how to do "long division" ?

8. ganeshie8

|dw:1440095909160:dw|

9. sjg13e

lol, i'm not gonna lie, it's been a while. but i can do it! thanks for answering. The way I initially approached it was by doing $2\int\limits_{}^{}x * \frac{ 1 }{ 2x +1 }$ and then using $uv - \int\limits_{}^{}vdu$ to solve. so maybe that's why i didn't initially think of doing long division

10. ganeshie8

that gives you back the original integrand haha!

11. sjg13e

yeah that's why i was like what am i doing wrong?? haha

12. ganeshie8

ikr! review this quick for long division https://www.khanacademy.org/math/algebra2/polynomial_and_rational/dividing_polynomials/v/polynomial-division

13. sjg13e