Matematika II - LS 24/25 Course Materials & Test Answers | moodle.czu.cz

Spočtěte neurčitý integrál

$\displaystyle\int\frac{x\cdot 5^x+1}{6x}dx.$ \displaystyle\int\frac{x\cdot 5^x+1}{6x}dx.

$\displaystyle\frac{5^x+x\cdot 5^x\cdot \ln5}{6}+C$ \displaystyle\frac{5^x+x\cdot 5^x\cdot \ln5}{6}+C

$\displaystyle\frac{5^x+2(x-1)}{6(x-1)}+C$ \displaystyle\frac{5^x+2(x-1)}{6(x-1)}+C

$\displaystyle\frac{x\cdot 5^x+2\ln5}{6x\cdot \ln 5}+C$ \displaystyle\frac{x\cdot 5^x+2\ln5}{6x\cdot \ln 5}+C

$\displaystyle\frac{(x-1)5^x+x}{3x^2}+C$ \displaystyle\frac{(x-1)5^x+x}{3x^2}+C

$\displaystyle\frac{5^x+\ln5\cdot \ln |x|}{6\ln 5}+C$ \displaystyle\frac{5^x+\ln5\cdot \ln |x|}{6\ln 5}+C

$\displaystyle\frac{x^2\cdot 5^x\cdot \ln5-1}{6x^2}+C$ \displaystyle\frac{x^2\cdot 5^x\cdot \ln5-1}{6x^2}+C

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