1 / | | (3 - 2*x)*atan(x)*1 dx | / 0
Integral(3 - 2*x*atan(x)*1, (x, 0, 1))
There are multiple ways to do this integral.
Rewrite the integrand:
Integrate term-by-term:
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:
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 a constant is the constant times the variable of integration:
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
So, the result is:
So, the result is:
The result is:
Use integration by parts:
Let and let .
Then .
To find :
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 when :
So, the result is:
The result is:
Now evaluate the sub-integral.
Rewrite the integrand:
Integrate term-by-term:
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
So, the result is:
The integral of is .
The result is:
The integral of a constant is the constant times the variable of integration:
The result is:
Rewrite the integrand:
Integrate term-by-term:
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:
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 a constant is the constant times the variable of integration:
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
So, the result is:
So, the result is:
The result is:
Add the constant of integration:
The answer is:
/ / 2\ | 3*log\1 + x / 2 | (3 - 2*x)*atan(x)*1 dx = C + x - atan(x) - ------------- - x *atan(x) + 3*x*atan(x) | 2 /
3*log(2) pi 1 - -------- + -- 2 4
=
3*log(2) pi 1 - -------- + -- 2 4
Use the examples entering the upper and lower limits of integration.