tex]Спасибо!...

May 2022 1 8 Report

Найти неопределенные интегралы:

A) ∫([tex]3^{x}[/tex]-[tex]\frac{1}{x}[/tex]+[tex]\frac{4}{cos^{2}x }[/tex])dx

Б) ∫[tex]\frac{dx}{x^{2}+4 }[/tex]

В) ∫[tex]\frac{dx}{x^{2}-25 }[/tex]

Спасибо!

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NNNLLL54

Verified answer

$1)\; \; \int (3^{x}-\frac{1}{x}+\frac{4}{cos^2x})\, dx=\frac{3^{x}}{ln3}-ln|x|+4\, tgx+C\; ;\\\\\\2)\; \; \int \frac{dx}{x^2+4}=\frac{1}{2}\cdot arctg\frac{x}{2}+C\; ;\\\\\\3)\; \; \int \frac{dx}{x^2-25}=\frac{1}{10}\cdot ln\Big |\frac{x-5}{x+5}\Big |+C\; .$

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