Question

Calcule as Integrais Indefinidas:

A) x + (1/x^3) dx


B) 2senx dx


C) 2x - (1/2) dx

Answer 1

a)

$y=x+\frac{1}{x^3}$

$\maltese~y'=1-\frac{3}{x^4}~\maltese$

b)

$y=2sin(x)$

$\maltese~y'=2cos(x)~\maltese$

c)

$y=2x-\frac{1}{2}$

$\maltese~y'=2~\maltese$

Answer 2

$A) \\ \int\ {x+ \frac{1}{x^3} } \, dx \\ \int\ {x} \, dx + \int \frac{1}{x^3} dx = \frac{x^2}{2} - \frac{1}{2x^2} + K$

$B) \\ \int 2sen(x) dx \\ \\ 2\int sen(x)dx = -2cos(x) + K$

$C) \\ \int 2x - \frac{1}{2} dx \\ \\ 2\int x dx - \frac{1}{2} \int dx = x^2 - \frac{x}{2} + K$