1 / | | / 3 \ | |x sin(5*x)| | |-- + --------| dx | \3 5 / | / 0
Integral(x^3/3 + sin(5*x)/5, (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 is when :
So, the result is:
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:
The result is:
Add the constant of integration:
The answer is:
/ | | / 3 \ 4 | |x sin(5*x)| cos(5*x) x | |-- + --------| dx = C - -------- + -- | \3 5 / 25 12 | /
37 cos(5) --- - ------ 300 25
=
37 cos(5) --- - ------ 300 25
Use the examples entering the upper and lower limits of integration.