Задача 15162 ...

Partnerservis1

20.04.2017

найти неопределенный интеграл 1)∫(2x-1)^2/x dx 2)∫1/√1-y2 + 1/y2 dy 3)∫(4x3+25+ 1/ cosx) dx 4)∫(7 sin x + 7/sin2x+ 7/sin2x) dx

SOVA

20.04.2017

★

1)∫(2x–1)^2dx/x =∫(4x^2-4x+1)dx/x=
=4∫xdx-4∫dx+∫dx/x=
=(4x^2/2) -4x+ln|x|+C=2x^2-4x+ln|x|+C;
2)∫(1/√(1–y^2) + 1/y^2) dy=arcsiny-(1/y)+C;
3)∫(4x^3+2^x+ (1/ cosx)) dx=
=(4x^4/4) + (2^x)/ln2+ ln(tg|(x/2)+(π/4)|) +C;
4)∫(7sin x + 7/sin^2x+ 7/sinx) dx =
=7*(-cosx)+7*(-ctgx)+7ln(tg|(x/2)| +C=
=-7cosx-7ctgx+7ln(tg|(x/2)| +C;