1 / | | atan(4*x) dx | / 0
Integral(atan(4*x), (x, 0, 1))
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:
Add the constant of integration:
The answer is:
/ / 2\ | log\1 + 16*x / | atan(4*x) dx = C - -------------- + x*atan(4*x) | 8 /
log(17) - ------- + atan(4) 8
=
log(17) - ------- + atan(4) 8
-log(17)/8 + atan(4)
Use the examples entering the upper and lower limits of integration.