1 / | | 2*x - 1 | 3 dx | / 0
Integral(3^(2*x - 1), (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 an exponential function is itself divided by the natural logarithm of the base.
So, the result is:
Now substitute back in:
Rewrite the integrand:
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 an exponential function is itself divided by the natural logarithm of the base.
So, the result is:
Now substitute back in:
So, the result is:
Rewrite the integrand:
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 an exponential function is itself divided by the natural logarithm of the base.
So, the result is:
Now substitute back in:
So, the result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | 2*x - 1 | 2*x - 1 3 | 3 dx = C + -------- | 2*log(3) /
4 -------- 3*log(3)
=
4 -------- 3*log(3)
4/(3*log(3))
Use the examples entering the upper and lower limits of integration.