Помогите под оч срочно надо полное решение.. Created by zar88. algebra-ru

Помогите под оч срочно надо полное решение...

zar88 @zar88

July 2022 1 8 Report

Помогите под оч срочно надо полное решение.

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NNNLLL54

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$1)\quad \int \frac{x^2}{3+x^2}dx=\int \frac{x^2+3-3}{3+x^2} dx=\int (\frac{x^2+3}{3+x^2} +\frac{-3}{3+x^2} )dx=\\\\=\int (1-\frac{3}{3+x^2})dx=x-3\cdot \frac{1}{\sqrt3}\cdot arctg\frac{x}{\sqrt3}+C=x-\sqrt3\cdot arctg \frac{x\sqrt3}{3} +C;\\\\2)\quad \int \limits _0^1\frac{dx}{1+x} =[\; t=1+x\; ;\; dt=dx\; ,\; t_1=1+0=1\; ,\; t_2=1+1=2\; ]=\\\\=\int \limits _1^2\frac{dt}{t}=ln|t|\; |_1^2=ln2-\underbrace {ln1}_0=ln2\; ;$

$3)\quad \int (3x-1)^5dx=[\; t=3x-1\; ,\; dt=3\, dx\; ]=\\\\=\int t^5\cdot \frac{dt}{3}=\frac{1}{3}\cdot \frac{t^6}{6}+C=\frac{1}{18}\cdot (3x-1)^6+C\; ;$

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