całka
: 10 lut 2009, o 13:32
Oblicz
\(\displaystyle{ \int_{}^{}}\)\(\displaystyle{ \frac{ x^{2}dx }{x ^{3}+1 }}\)
\(\displaystyle{ \int_{}^{}}\)\(\displaystyle{ \frac{ x^{2}dx }{x ^{3}+1 }}\)
\(\displaystyle{ \begin{cases}
t=x^3+1 \\
dt=3x^2 dx \\
\frac{dt}{3}=x^2 dx
\end{cases}
\newline
=\int \frac{\frac{dt}{3}}{t}=\frac{1}{3}\int \frac{dt}{t}=\frac{1}{3}ln(t)+c=\frac{1}{3}ln(x^3+1)+c}\)