2 / | | 3 | (4*x + 3) dx | / -1
Integral((4*x + 3)^3, (x, -1, 2))
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 is when :
So, 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 is when :
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 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 is the constant times the variable of integration:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | 4 | 3 (4*x + 3) | (4*x + 3) dx = C + ---------- | 16 /
Use the examples entering the upper and lower limits of integration.