Polsl-Notes/AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md

Obliczyć całki.

1

\int x^{2}(1-x)dx=\int x^{2}-x^{3}dx=

9.

$$\int x\sqrt{x}\ dx= \int x^{\frac{3}{2}}dx= \frac{x^{\frac{5}{2}}}{\frac{5}{2}}+c=\frac{2x^{\frac{5}{2}}}{5}+c$$ 18.

\int (4^{x}+2^{-x})dx=\frac{4x}{\ln 4}+ \int (\frac{1}{2})^{x}dx=\frac{4^{x}}{\ln 4}+\frac{(\frac{1}{2})^{x}}{\ln \frac{1}{2}}+c