Question

Sorry, wrong question! the integral of (x(ln(1+x))dx

Answer 1

integration by parts

Answer 2

xdx=(x^2)/2+c

Answer 3

?

Answer 4

have you done integration by parts before?

Answer 5

Yes, but I cannot figure this one out. What shoul u be? ln(1+x)?

Answer 6

\[u=\ln(1+x)\]
\[dv=xdx\]

Answer 7

Used that, but just keeps growing.

Answer 8

how

...

Answer 9

\[du=\frac{1}{1+x}dx\]

\[v=\frac{x^2}{2}\]

\[\int x\ln(1+x)dx=\frac{x^2}{2}\ln(1+x)-\int\frac{x^2}{2(1+x)}dx\]

Answer 10

right?

Answer 11

a little algebra gives us

\[\frac{x^2}{2(1+x)}=\frac{1}{2(1+x)}+\frac{x}{2}-\frac{1}{2}\]

Answer 12

partial fractions?

Answer 13

long division

Answer 14

you don't use partial fractions when the power if the numerator is >= power of the denominator

Answer 15

thanks got it now

Answer 16

good