task/29580419
Найти все первообразные для функции
∫(eˣ +5sinx)dx =∫eˣdx +∫5sinxdx =∫eˣdx +5∫sinxdx =eˣ - 5cosx +C . → A)
∫(6x-7)⁴dx =(1/6)*∫(6x-7)⁴d(6x-7) =(1/6)*(6x-7)⁴⁺¹ /(4+1) +C=(6x-7)⁵ /30 +C. → E)
∫( (1/(2x -1)) dx= (1/2)*∫( (1/(2x -1)) d(2x -1) = (1/2)*Ln/(2x -1)+ C . → E)
∫ ( e^( x / 3 +4) - 2sinx )dx =∫ ( e^( x / 3 +4)dx - ∫ 2sinx )dx =
= 3∫ ( e^( x / 3 +4)d(x / 3 +4) - 2∫ sinxdx =3e^( x / 3 +4) - 2cosx +C. → B)
∫( (5/(x -5) -5sin(5x -1) ) dx= 5*∫( (1 /(x -5)) d(x -5) - ∫ 5sin(5x -1) dx =
=5ln(x -5) - ∫ sin(5x -1) d(5x-1) +C = 5ln(x -5) + cos(5x -1) +C . → A)
Удачи !