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 log(1+x)/x^2
-
Integral of (x-x^2)
-
Integral of x/(x^2+4*x+8)
-
Integral of x*(x+1)^1/2
-
Identical expressions
- a^(5x)+e^(5x)
- a to the power of (5x) plus e to the power of (5x)
- a(5x)+e(5x)
- a5x+e5x
- a^5x+e^5x
- a^(5x)+e^(5x)dx
-
Similar expressions
- a^(5x)-e^(5x)
Integral of a^(5x)+e^(5x) dx
The solution
You have entered
[src]
1 / | | / 5*x 5*x\ | \a + E / dx | / 0
$$\int\limits_{0}^{1} \left(a^{5 x} + e^{5 x}\right)\, dx$$
Integral(a^(5*x) + E^(5*x), (x, 0, 1))
The answer (Indefinite)
[src]
/ 5*x
| a
|------ for log(a) != 0
$$\int \left(a^{5 x} + e^{5 x}\right)\, dx = C + \frac{\begin{cases} \frac{a^{5 x}}{\log{\left(a \right)}} & \text{for}\: \log{\left(a \right)} \neq 0 \\5 x & \text{otherwise} \end{cases}}{5} + \frac{e^{5 x}}{5}$$
The answer
[src]
// 5 \
5 || 1 a |
1 e ||- -------- + -------- for Or(And(a >= 0, a < 1), a > 1)|
- - + -- + |< 5*log(a) 5*log(a) |
5 5 || |
|| 1 otherwise |
\\ /
$$\begin{cases} \frac{a^{5}}{5 \log{\left(a \right)}} - \frac{1}{5 \log{\left(a \right)}} & \text{for}\: \left(a \geq 0 \wedge a < 1\right) \vee a > 1 \\1 & \text{otherwise} \end{cases} - \frac{1}{5} + \frac{e^{5}}{5}$$
=
=
// 5 \
5 || 1 a |
1 e ||- -------- + -------- for Or(And(a >= 0, a < 1), a > 1)|
- - + -- + |< 5*log(a) 5*log(a) |
5 5 || |
|| 1 otherwise |
\\ /
$$\begin{cases} \frac{a^{5}}{5 \log{\left(a \right)}} - \frac{1}{5 \log{\left(a \right)}} & \text{for}\: \left(a \geq 0 \wedge a < 1\right) \vee a > 1 \\1 & \text{otherwise} \end{cases} - \frac{1}{5} + \frac{e^{5}}{5}$$
-1/5 + exp(5)/5 + Piecewise((-1/(5*log(a)) + a^5/(5*log(a)), (a > 1)∨((a >= 0)∧(a < 1))), (1, True))
Use the examples entering the upper and lower limits of integration.