If x has the power 2 then you want the integral of x2, I think. When you integrate this you get : x3/3 , plus a constant.
let u = x du=dx let dv= e^x v=e^x ∫ xe^(x)dx = xe^x - ∫ e^(x)dx = xe^x - e^x = e^x ( x-1 ) + c
xe^(5x) is an expression involving x and Euler's constant
-(10/x)
To integrate a function you find what the function you have is the derivative of. for example the derivative of x^2 is 2x. so the integral of 2x is x^2.
{xe^x dx integrate by parts let f(x) = x so f'(x) = 1 and g(x) = e^x so g'(x) = e^x so.. f(x)*g(x) - {(g(x)*f'(x)) dx therefore xe^x - {(e^x * 1) dx so.. xe^x - e^x + C factorize so... (x-1)e^x + C
e^x/1-e^x
integrate(x5x dx) simplifies to integrate(5x^2 dx), and using the power rule of integration, add one to the power of x and divide the term by that number. Thus, x5x dx integrated is (5/3)x^3
x-1 = 1/x ∫1/x dx = ln x + C
If x has the power 2 then you want the integral of x2, I think. When you integrate this you get : x3/3 , plus a constant.
I can't integrate a-x /x-3 ?
Do it by parts. Int(u.dv) = u.v - int(v.du) Let x = u, then dx = du. Let e^x = dv, then v = e^x. Plug into formula: xe^x - int(e^x.dx) = x.e^x - e^x or e^x(x-1)+C
let u = x du=dx let dv= e^x v=e^x ∫ xe^(x)dx = xe^x - ∫ e^(x)dx = xe^x - e^x = e^x ( x-1 ) + c
xe^(5x) is an expression involving x and Euler's constant
Xenon (Xe)
Apparently that can't be solved with a finite number of so-called "elementary functions". You can get the beginning of the series expansion here: http://www.wolframalpha.com/input/?i=integrate+x^x
-(10/x)