Home
Class 12
MATHS
Integrate the function x^2logx...

Integrate the function `x^2logx`

Text Solution

Verified by Experts

Let `f(x) = logx and g(x) = x^2`
`intx^2logx = int f(x)g(x)dx`
We know,
`int f(x)g(x)dx=f(x)intg(x)dx-int(f'(x)intg(x)dx)dx`
Here, `f'(x) = d/dx(logx) = 1/x`
So,`intx^2logx = (logx)intx^2dx-int((1/x)intx^2dx)dx`
`=(x^3logx)/3+c-intx^2/3dx`
`=(x^3logx)/3-x^3/9+c`
Promotional Banner

Similar Questions

Explore conceptually related problems

Integrate the functions x log2x

Integrate the functions x log x

Integrate the functions x(log x)^(2)

Integrate the functions ((log x)^(2))/(x)

Integrate the functions ((1+log x)^(2))/(x)

Integrate the functions x^(2)e^(x)

Integrate the functions e^(2x)sin x

Integrate the functions (x^(2)+1)log x

Integrate the functions x sec^(2)x

Integrate the functions (x^(2))/(1-x^(6))