vault backup: 2023-09-11 15:47:34

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

@@ -74,4 +74,11 @@ $$
 ## 17.
 $$\int \frac{\sqrt[3]{x}-1}{\sqrt[6]{x}-1}dx=\int\frac{x^{\frac{1}{3}}-1}{x^{\frac{1}{6}}-1}dx=\int\frac{x^{\frac{1}{3}}}{x^{\frac{1}{6}}-1}-\int\frac{1}{x^{\frac{1}{6}}-1}=$$
 ## 18.
-$$\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$$
+$$\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$$
+## 19.
+$$
+\begin{gathered}
+\int5^{x}e^{x}dx= \int(5e)^x
+
+\end{gathered}
+$$

AMiAL/Ściągi.md

@@ -1,8 +1,9 @@
 
 ## Tabela funkcji trygonometrycznych
+
 |rad|0|$\frac{\pi}{6}$|$\frac{\pi}{4}$|$\frac{\pi}{3}$|$\frac{\pi}{2}$|$\pi$|
 |:-|-|-|-|-|-|-|
-|deg|0°|30°|45°|60°|90°|180°|
+|deg|$0°$|$30°$|$45°$|$60°$|$90°$|$180°$|
 |$\sin{\alpha}$|$0$|$\frac{1}{2}$|$\frac{1}{2}$|$\frac{1}{2}$|$1$|$0$|
 |$\cos{\alpha}$|$1$|$\frac{\sqrt{3}}{2}$|$\frac{\sqrt{2}}{2}$|$\frac{1}{2}$|$0$|$-1$|
 |$\tan{\alpha}$|$0$|$\frac{\sqrt{3}}{3}$|1|$\sqrt{3}$|$-$|$0$|