Найти неопределенный интеграл [tex]arctg\sqrt{2x-1} dx[/tex]. Created by sobakazabiyaka. algebra-ru

tex]...

sobakazabiyaka @sobakazabiyaka

November 2021 1 33 Report

Найти неопределенный интеграл
[tex]arctg\sqrt{2x-1} dx[/tex]

Answers & Comments

NNNLLL54

Verified answer

$\int arctg\sqrt{2x-1}\, dx=\Big[\ t^2=2x-1\ ,\ t=\sqrt{2x-1}\ ,\ x=\dfrac{t^2+1}{2}\ ,\ dx=t\, dt\Big]=\\\\\\=\int arctgt\cdot t\, dt=\Big[\ u=arctgt\ ,\ du=\dfrac{dt}{1+t^2}\ ,\ dv=t\, dt\ ,v=\dfrac{t^2}{2}\ ,\\\\\\\int u\, dv=uv-\int v\, du\ \Big]=\dfrac{t^2}{2}\cdot arctgt-\dfrac{1}{2}\int\dfrac{t^2\, dt}{1+t^2}=\\\\\\=\dfrac{t^2}{2}\cdot arctgt-\dfrac{1}{2}\int\Big(1-\dfrac{1}{1+t^2}\Big)\, dt=\dfrac{t^2}{2}\cdot arctgt-\dfrac{1}{2}\cdot \Big(t-arctgt\Big)+C=$

$=\dfrac{2x-1}{2}\cdot arctg\sqrt{2x-1}-\dfrac{1}{2}\cdot \Big(\sqrt{2x-1}-arctg\sqrt{2x-1}\Big)+C=$

1 votes Thanks 0

Answers & Comments

Verified answer

prodolzhite dialog hotya by 3 4 voprosa

tex]...

sostavte predlozhenie so slovosochetaniem kn ashyldy5e9a057563ded4663388452bb4deb7ae 40601

sostavte predlozhenie na kaz yazyke so slovom auatty

tex]...

sostavte predlozheniya s etimi chislitelnymi 6 mynan 500 178 10746fc38a5a004584cab50cfbe8cabc08d 34776

kakoj metall nelzya poluchit metodom vosstanovleniya metalla vodoroda a natrij

est li v etom predlozhenii prilozhenie i vdrug neozhidanno kak poslednij podaro

tex]...

tex]...

рекомендуемые вопросы

Helpful Links

Helpful Social