Задача 15161 ...

Partnerservis1

20.04.2017

Решение интегралов: 1) ∫1/((6-8x)5) dx; 2) ∫1/(5t-27) dx; 3)∫614-13xdx; 4)∫cos(x/14-19)dx; 5)∫tg2x/sin2x dx; 6) ∫4x4 – 2x3 +x2/x2 dx

SOVA

20.04.2017

★

1) ∫dx/((6–8x)^5) =(-1/8) ∫(6-8x)^(-5)d(6-8x)=
=(-1/8)*(6-8x)^(-5+1)/(-5+1)+C=1/(32*(6-8x)^4)+C;
2) ∫1/(5t–27) dt=(1/5)∫d(5t-27)/(5t–27) =(1/5)* ln|5t-27|+C;
3)∫6^(14–13x)dx=(-1/13)*∫6^(14–13x)dx=
=(-1/13)*(6^(14-13x)/ln6) +C=-(6^(14-13x))/(13ln6)+C;
4)∫cos((x/14)–19)dx=14∫cos((x/14)–19)d((x/14) -19)=
=14sin((x/14)–19) + C;
5)∫(tg^2x/sin^2x) dx=∫1/cos^2x dx= tgx+C;
6) ∫(4x^4 – 2x^3 +x^2)dx/x^2 = ∫(4x^2 – 2x +1)dx=
=(4x^3/3) -x^2+x+C.