tausinv

Verified answer

1) S2*sinx dx = 2*Ssinx dx = -2*cosx + c
2) S5\x *dx = 5*S1\x *dx = 5*lnx + c;
3) S(x^2  -2x + 3)dx = Sx^2 dx - 2Sx dx + 3*S 1 * dx =
= (x^3)/3 - x^2 + 3x + c
4) S1\2x *dx = 1\2 *S1\x *dx = 1\2 *lnx +c
5) S(x^3 + 3) dx = (x^4)/4 + 3x при подстановке
(4 + 6) - (1\4 + 3) = 13 - 1\4 = 12 и 3\4
6) Ssin3xdx = 1\3 * Ssin3x d3x = - 1\3 *cos3x  при подстановке
0 - (-1\3) = 1\3
7)S x^1\2 + x^(4\3) dx = 2\3 * x^(3\2) + 3\7 * x^(7\3)  при подстановке
2\3 + 3\7 - 0 = 23\21 = 1 и 2\21
8) S sinx\cos^2(x) dx = - S 1\cos^2(x) dcosx  =
cosx = t - замена переменной
= - S 1\t^2 dt = 1\t + c = 1\cosx + c