Integral of 2^(3*x) dx
The solution
Detail solution
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Let u=3x.
Then let du=3dx and substitute 3du:
∫32udu
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The integral of a constant times a function is the constant times the integral of the function:
∫2udu=3∫2udu
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The integral of an exponential function is itself divided by the natural logarithm of the base.
∫2udu=log(2)2u
So, the result is: 3log(2)2u
Now substitute u back in:
3log(2)23x
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Now simplify:
3log(2)8x
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Add the constant of integration:
3log(2)8x+constant
The answer is:
3log(2)8x+constant
The answer (Indefinite)
[src]
/
| 3*x
| 3*x 2
| 2 dx = C + --------
| 3*log(2)
/
∫23xdx=3log(2)23x+C
The graph
3log(2)7
=
3log(2)7
Use the examples entering the upper and lower limits of integration.