1 / | | sin(2 + 3*log(x)) | ----------------- dx | x | / 0
Integral(sin(2 + 3*log(x))/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:
The integral of sine is negative cosine:
So, the result is:
Now substitute back in:
Let .
Then let and substitute :
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 sine is negative cosine:
So, the result is:
Now substitute back in:
So, the result is:
Now substitute back in:
Add the constant of integration:
The answer is:
/ | | sin(2 + 3*log(x)) cos(2 + 3*log(x)) | ----------------- dx = C - ----------------- | x 3 | /
1 cos(2) 1 cos(2) <- - - ------, - - ------> 3 3 3 3
=
1 cos(2) 1 cos(2) <- - - ------, - - ------> 3 3 3 3
AccumBounds(-1/3 - cos(2)/3, 1/3 - cos(2)/3)
Use the examples entering the upper and lower limits of integration.