vault backup: 2023-03-03 09:17:30

AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md

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