Integral of 5^(2*x) dx
The solution
Detail solution
-
Let u=2x.
Then let du=2dx and substitute 2du:
∫25udu
-
The integral of a constant times a function is the constant times the integral of the function:
∫5udu=2∫5udu
-
The integral of an exponential function is itself divided by the natural logarithm of the base.
∫5udu=log(5)5u
So, the result is: 2log(5)5u
Now substitute u back in:
2log(5)52x
-
Now simplify:
2log(5)25x
-
Add the constant of integration:
2log(5)25x+constant
The answer is:
2log(5)25x+constant
The answer (Indefinite)
[src]
/
| 2*x
| 2*x 5
| 5 dx = C + --------
| 2*log(5)
/
∫52xdx=2log(5)52x+C
The graph
log(5)12
=
log(5)12
Use the examples entering the upper and lower limits of integration.