Integrate the following
(x^5 - 2)dx
INT x^5 dx - 2INT dx
surely you can do that.
x^5 dx --> (1/6)x^6
-2 dx --> -2x
so
(1/6)x^6 - 2x + C
To integrate the expression (x^5 - 2) dx, we can use the power rule of integration. According to the power rule, the integral of x^n dx, where n is any constant, is (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.
In this case, we can break down the integral of (x^5 - 2) dx as the sum of two integrals:
∫(x^5 - 2) dx = ∫x^5 dx - ∫2 dx
Now let's calculate each integral separately:
∫x^5 dx:
By the power rule, integrating x^5 gives us (1/(5+1)) * x^(5+1) + C = (1/6) * x^6 + C.
∫2 dx:
Since 2 is a constant, the integral of a constant is the constant multiplied by x, so ∫2 dx = 2x + C.
Combining both results, we have:
∫(x^5 - 2) dx = (1/6) * x^6 + 2x + C,
where C is the constant of integration.