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vault backup: 2023-03-10 09:03:26

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VectorKappa
2023-03-10 09:03:26 +01:00
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commit 484d751315
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2
.obsidian/workspace.json vendored
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@@ -6,6 +6,7 @@
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AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md
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@@ -26,7 +26,7 @@ $$\int x\sqrt{x}\ dx=
\int x^{\frac{3}{2}}dx= \frac{x^{\frac{5}{2}}}{\frac{5}{2}}+c=\frac{2x^{\frac{5}{2}}}{5}+c$$ \int x^{\frac{3}{2}}dx= \frac{x^{\frac{5}{2}}}{\frac{5}{2}}+c=\frac{2x^{\frac{5}{2}}}{5}+c$$
## 10. ## 10.
$$ $$
\int x\sqrt[4]{x^{3}}dx = \int\sqrt[4]{x^{7}}dx=\int x^{\frac{7}{4}}dx= \int x\sqrt[4]{x^{3}}dx = \int\sqrt[4]{x^{7}}dx=\int x^{\frac{7}{4}}dx=\frac{x^{\frac{11}{4}}}{\frac{11}{4}}+C=\frac{4x^{\frac{11}{4}}}{11}+C=\frac{8\sqrt[4]{x^{3}}}{11}+C
$$ $$
## 18. ## 18.
$$\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$$