∫ (x^5+∛(x^2)+(1/∛x))dx=
= ∫ x^5dx + ∫ x^(2/3)dx+ ∫ x^(-1/3)dx=
=(x^6/6) +x^(5/3)/(5/3) +x^(2/3)/(2/3)+C=
= (x^6/6) +(3/5)*x^(5/3) +(3/2)*x^(2/3)+C=
= (x^6/6) +(3/5)*x*∛(x^2) +(3/2)*∛(x^2)+C
м)
∫ (7x-2)^4dx= ∫ (7x-2)^(4)*(1/7)d(7x-2)=
=(1/7) ∫ u^4du=(1/7)(u^5/5) + C= (1/35)*(7x-2)^5 + C
u=7x-2
du=(7x-2)`=7dx ⇒ dx=(1/7)d(7x-2)
т)
=2 ∫ dx/(1+x^2)-3 ∫ dx/sqrt(1-x^2)=
=2arctgx - 3 arcsinx + C