Rozwiązanie:
[tex]\bold{(a)}[/tex]
[tex]$\int \Big(1-\frac{1}{x^{2}}\Big)\sqrt{x\sqrt{x}} \ dx=\int x^{\frac{3}{4}}-x^{-\frac{5}{4}} \ dx=\frac{4}{7}x^{\frac{7}{4}}+4x^{-\frac{1}{4}}+C[/tex]
[tex]\bold{(b)}[/tex]
[tex]$\int \sqrt[3]{1-3x} \ dx=\left|\begin{array}{cc}u=1-3x\\du=-3 \ dx\end{array}\right|=-\frac{1}{3}\int u^{\frac{1}{3}} \ du=-\frac{1}{4}u^{\frac{4}{3}}+C=\frac{1}{4}(1-3x)^{\frac{4}{3}}+C[/tex]
[tex]\bold{(c)}[/tex]
[tex]$\int xe^{-x^{2}} \ dx=\left|\begin{array}{cc}u=-x^{2}\\-du=2x \ dx\end{array}\right|=-\frac{1}{2}\int e^{u} \ du=-\frac{1}{2}e^{u}+C=-\frac{1}{2}e^{-x^{2}}+C[/tex]
