Tuesday, October 23, 2012

f(x) = 1/x + 6x^2 find the integral for f(x)

The indefinite integral
is:


Int f(x)dx = Int (1/x  +
6x^2)dx


We'll use the additive property of
integral:


Int (1/x  + 6x^2)dx = Int (1/x)dx  + Int
(6x^2)dx


Int (1/x)dx = ln |x| +
C


Int (6x^2)dx = 6 Int x^2dx


6
Int x^2dx = 6x^3/3 + C


6 Int x^2dx = 2x^3 +
C


Int (1/x  + 6x^2)dx = ln |x| + 2x^3 +
C


Note: We've considered the absolute value of x, because
it is not assigned an interval of values for x.

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