1 / | | 13*x*atan(x)*1 dx | / 0
Integral(13*x*atan(x)*1, (x, 0, 1))
The integral of a constant times a function is the constant times the integral of the function:
Use integration by parts:
Let and let .
Then .
To find :
The integral of is when :
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant is the constant times the variable of integration:
The integral of a constant times a function is the constant times the integral of the function:
The integral of is .
So, the result is:
The result is:
So, the result is:
So, the result is:
Add the constant of integration:
The answer is:
/ 2 | 13*x 13*atan(x) 13*x *atan(x) | 13*x*atan(x)*1 dx = C - ---- + ---------- + ------------- | 2 2 2 /
13 13*pi - -- + ----- 2 4
=
13 13*pi - -- + ----- 2 4
Use the examples entering the upper and lower limits of integration.