Obliczyć całki nieoznaczone.

[faraus]

Obliczyć całki:
1)\(\displaystyle{ \int_{}^{} \frac{dx}{1+9x ^{2} }}\)
2)\(\displaystyle{ \int_{}^{} \frac{x ^{2}dx }{x ^{6}+1 }}\)
3)\(\displaystyle{ \int_{}^{} \frac{dx}{ \sqrt{4-x ^{2} } }}\)

[fermat]

3)\(\displaystyle{ \int_{}^{} \frac{dx}{ \sqrt{4-x ^{2} } }}\)

\(\displaystyle{ ... = \int \frac {dx}{\sqrt {2^{2} - x^{2}}} = arcsin \frac{x}{2} + C}\)-- 14 lut 2009, o 13:22 --

2)\(\displaystyle{ \int_{}^{} \frac{x ^{2}dx }{x ^{6}+1 }}\)

\(\displaystyle{ x^{3} = t}\)
\(\displaystyle{ \frac {1}{3}dt = x^{2}dx}\)
\(\displaystyle{ ... = \frac {1}{3} \int \frac{1}{t^{2} + 1}dt = \frac {1}{3} arctgt + C = \frac{1}{3} arctg x^{3} + C}\)

[Dedemonn]

1)

\(\displaystyle{ \begin{bmatrix} x = \frac{1}{3}t \\ dx = \frac{1}{3}dt \end{bmatrix} = \frac{1}{3} \int \frac{dt}{1+t^2} = \frac{1}{3}arctg3x + C}\)