1 / | | / 3 \ | |atan(2*x) - --*atan(2*x)| dx | | 4 | | \ x / | / 0
Integral(atan(2*x) - 3/x^4*atan(2*x), (x, 0, 1))
Integrate term-by-term:
The integral of a constant times a function is the constant times the integral of the function:
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:
There are multiple ways to do this integral.
Let .
Then let and substitute :
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 a constant times a function is the constant times the integral of the function:
The integral of is .
So, the result is:
Now substitute back in:
So, the result is:
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 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 substitute back in:
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant times a function is the constant times the integral of the function:
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 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 integral of is when :
The result is:
Rewrite the integrand:
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant times a function is the constant times the integral of the function:
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 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 integral of is when :
The result is:
Rewrite the integrand:
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant times a function is the constant times the integral of the function:
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 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 integral of is when :
The result is:
So, the result is:
So, the result is:
So, the result is:
There are multiple ways to do this integral.
Let .
Then let and substitute :
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:
Now substitute back in:
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:
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 \ 1 / 2\ 17*log\1 + 4*x / atan(2*x) | |atan(2*x) - --*atan(2*x)| dx = C + -- + 4*log\x / - ---------------- + x*atan(2*x) + --------- | | 4 | 2 4 3 | \ x / x x | /
Use the examples entering the upper and lower limits of integration.