1 / | | /3 \ | |- - 2*sin(5*x) + 1| dx | \x / | / 0
Integral(3/x - 2*sin(5*x) + 1, (x, 0, 1))
Integrate term-by-term:
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 sine is negative cosine:
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 result is:
The integral of a constant is the constant times the variable of integration:
The result is:
Add the constant of integration:
The answer is:
/ | | /3 \ 2*cos(5*x) | |- - 2*sin(5*x) + 1| dx = C + x + 3*log(x) + ---------- | \x / 5 | /
Use the examples entering the upper and lower limits of integration.