Question

Integral..Could you help me,please?

Answer 1

as we know, the integral of
`x^(n)` is
`(x^(n+1) )/(n+1)`

so, the integral of x.
`2^(x)` will be found as follows:

here, we will use a trick called 'integration by parts'

let x = u and
`2^(x)` = v

∫uv dx = u∫v dx - ∫[(du/dx)* ∫v dx] dx

∫x.
`2^(x)` dx = x∫
`2^(x)` - ∫[(dx/dx) * ∫
`2^(x)` dx ] dx

∫x.
`2^(x)` dx = x*
`(2^(x+ 1))/(x+ 1)` - 1 *
`(2^(x + 1) )/(x + 1)`

=
`(2^(x) )/(x + 1)`( x - 1 )