2 proste calki do sprawdzenia

Macabre · Post autor: **Macabre** » 5 gru 2008, o 21:43

1)

\(\displaystyle{ \int_{}^{} (\frac{1-x}{x})^{2}dx= \int_{}^{}\frac{1-2x+x^{2}}{x^{2}}dx= \int_{}^{} x^{-2}dx-2 \int_{}^{} x^{-1}+ \int_{}^{} dx= \\ =-x^{-1}-2ln|x|+x+c}\)

2)

\(\displaystyle{ \int_{}^{} xsinxdx=}\)

u=x v'=sinx
u'=1 v=-cosx

\(\displaystyle{ =xcosx+ \int_{}^{} cosxdx= xcox+sinx}\)

Edit: poprawione, thx

soku11 · Post autor: **soku11** » 5 gru 2008, o 21:47

1) OK.
2)
\(\displaystyle{ \int \sin x\mbox{d}x=-\cos x+C}\)

Wiec znak sie nie zgadza.

Pozdrawiam.