[m] ∫^{1}_{0}\sqrt[7]{x^3}dx= ∫ ^{1}_{0}x^{\frac{3}{7}}dx=(\frac{x^{\frac{3}{7}+1}}{\frac{3}{7}+1})|^{1}_{0}=(\frac{x^{\frac{10}{7}}}{\frac{10}{7}})|^{1}_{0}=\frac{7}{10}\cdot (1^{\frac{10}{7}}-0^{\frac{10}{7}}=\frac{7}{10}=0,7[/m]
[m] ∫^{3}_{2}5^{2x}dx= ∫^{3}_{2}5^{2x}\cdot \frac{1}{2}dx=\frac{1}{2}\cdot ∫ ^{3}_{2}5^{2x}d(2x)=\frac{1}{2}\cdot (\frac{5^{2x}}{ln5})|^{3}_{2}=\frac{1}{2\cdot ln5}\cdot (5^{2\cdot 3}-5^{2\cdot 2})=\frac{625\cdot (24)}{2\cdot ln5}=[/m]
[m]=\frac{625\cdot (12)}{ ln5}=\frac{7500}{ ln5}.[/m]