Integral of exp((4*x)/3)-(2/exp(-x)) dx
The solution
Detail solution
-
Integrate term-by-term:
-
Let u=34x.
Then let du=34dx and substitute 43du:
∫43eudu
-
The integral of a constant times a function is the constant times the integral of the function:
-
The integral of the exponential function is itself.
∫eudu=eu
So, the result is: 43eu
Now substitute u back in:
43e34x
-
The integral of a constant times a function is the constant times the integral of the function:
∫(−e−x2)dx=−2∫e−x1dx
-
Let u=e−x.
Then let du=−e−xdx and substitute −du:
∫(−u21)du
-
The integral of a constant times a function is the constant times the integral of the function:
∫u21du=−∫u21du
-
The integral of un is n+1un+1 when n=−1:
∫u21du=−u1
So, the result is: u1
Now substitute u back in:
So, the result is: −2ex
The result is: −2ex+43e34x
-
Now simplify:
43e34x−2ex
-
Add the constant of integration:
43e34x−2ex+constant
The answer is:
43e34x−2ex+constant
The answer (Indefinite)
[src]
/
| 4*x
| / 4*x \ ---
| | --- | 3
| | 3 2 | x 3*e
| |e - ---| dx = C - 2*e + ------
| | -x| 4
| \ e /
|
/
∫(e34x−e−x2)dx=C−2ex+43e34x
The graph
4/3
5 3*e
- - 2*E + ------
4 4
−2e+45+43e34
=
4/3
5 3*e
- - 2*E + ------
4 4
−2e+45+43e34
Use the examples entering the upper and lower limits of integration.