Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of x^4/(1+x^2)
-
Integral of x^5/(x^2+1)
-
Integral of (tan(x))^2/(cos(x))^2
-
Integral of sqrt(x^2+1)*dx/x
-
Identical expressions
- two ^x*e^x
- 2 to the power of x multiply by e to the power of x
- two to the power of x multiply by e to the power of x
- 2x*ex
- 2^xe^x
- 2xex
- 2^x*e^xdx
Integral of 2^x*e^x dx
The solution
You have entered
[src]
1 / | | x x | 2 *E dx | / 0
$$\int\limits_{0}^{1} 2^{x} e^{x}\, dx$$
Integral(2^x*E^x, (x, 0, 1))
The answer (Indefinite)
[src]
/ | x x | x x 2 *e | 2 *E dx = C + ---------- | 1 + log(2) /
$$\int 2^{x} e^{x}\, dx = \frac{2^{x} e^{x}}{\log{\left(2 \right)} + 1} + C$$
The graph
The answer
[src]
1
1 + ------
log(2)
1 2
- ------------------- + -------------------
/ 1 \ / 1 \
|1 + ------|*log(2) |1 + ------|*log(2)
\ log(2)/ \ log(2)/
$$- \frac{1}{\left(1 + \frac{1}{\log{\left(2 \right)}}\right) \log{\left(2 \right)}} + \frac{2^{1 + \frac{1}{\log{\left(2 \right)}}}}{\left(1 + \frac{1}{\log{\left(2 \right)}}\right) \log{\left(2 \right)}}$$
=
=
1
1 + ------
log(2)
1 2
- ------------------- + -------------------
/ 1 \ / 1 \
|1 + ------|*log(2) |1 + ------|*log(2)
\ log(2)/ \ log(2)/
$$- \frac{1}{\left(1 + \frac{1}{\log{\left(2 \right)}}\right) \log{\left(2 \right)}} + \frac{2^{1 + \frac{1}{\log{\left(2 \right)}}}}{\left(1 + \frac{1}{\log{\left(2 \right)}}\right) \log{\left(2 \right)}}$$
-1/((1 + 1/log(2))*log(2)) + 2^(1 + 1/log(2))/((1 + 1/log(2))*log(2))
The graph
Use the examples entering the upper and lower limits of integration.