Question

Determine as primitivas das funções:

a) $x^{5}$

b) $7 x^{6}$

c) $4 x^{3}-3 x^{2}+1$

d) $x^{2/3}$

Answer 1

$\boxed{\int x^5dx=\frac{x^6}{6}+C} \\ \\ \boxed{\int 7x^6 dx=7 \int x^6 dx=7.\frac{x^7}{7}+C=x^7+C }\\ \\ \int (4x^3-3x^2+1) dx=4 \int x^3 dx-3 \int x^2 dx + \int dx=4.\frac{x^4}{4}-3.\frac{x^3}{3}+x+C= \\ \\ \boxed{x^4-x^3+x+C }\\ \\ \boxed{\int x^{\frac{2}{3}} dx=\frac{3x^{\frac{5}{3}}}{5}+C}$