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- Improper integral
- Double Integral
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- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(2+x^2)
- Integral of sin(w*t)^2
- Integral of sin(log(x))^2/x
- Integral of sin^n(x)
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Identical expressions
- sqrt(one +a^ two *exp(2x))
- square root of (1 plus a squared multiply by exponent of (2x))
- square root of (one plus a to the power of two multiply by exponent of (2x))
- √(1+a^2*exp(2x))
- sqrt(1+a2*exp(2x))
- sqrt1+a2*exp2x
- sqrt(1+a²*exp(2x))
- sqrt(1+a to the power of 2*exp(2x))
- sqrt(1+a^2exp(2x))
- sqrt(1+a2exp(2x))
- sqrt1+a2exp2x
- sqrt1+a^2exp2x
- sqrt(1+a^2*exp(2x))dx
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Similar expressions
- sqrt(1-a^2*exp(2x))
Integral of sqrt(1+a^2*exp(2x)) dx
The solution
You have entered
[src]
1 / | | _____________ | / 2 2*x | \/ 1 + a *e dx | / 0
$$\int\limits_{0}^{1} \sqrt{a^{2} e^{2 x} + 1}\, dx$$
Integral(sqrt(1 + a^2*exp(2*x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ / _____________\ _____________ / _____________\
| | / 2 2*x | / 2 2*x | / 2 2*x | 2
|- log\1 + \/ 1 + a *e / + 2*\/ 1 + a *e + log\-1 + \/ 1 + a *e / for a != 0
/ <
| | / 2*x\
| _____________ | log\e / otherwise
| / 2 2*x \
| \/ 1 + a *e dx = C + -------------------------------------------------------------------------------------------
| 2
/
$$-{{\log \left(\sqrt{a^2\,e^{2\,x}+1}+1\right)}\over{2}}+{{\log
\left(\sqrt{a^2\,e^{2\,x}+1}-1\right)}\over{2}}+\sqrt{a^2\,e^{2\,x}+
1}$$
The answer
[src]
/ / ________\ / ___________\ / ___________\ / ________\ | ___________ | / 2 | | / 2 2 | ________ | / 2 2 | | / 2 | | / 2 2 log\1 + \/ 1 + a / log\-1 + \/ 1 + a *e / / 2 log\1 + \/ 1 + a *e / log\-1 + \/ 1 + a / <\/ 1 + a *e + -------------------- + ------------------------ - \/ 1 + a - ----------------------- - --------------------- for And(a > -oo, a < oo, a != 0) | 2 2 2 2 | \ 1 otherwise
$$-{{\log \left(\sqrt{e^2\,a^2+1}+1\right)}\over{2}}+{{\log \left(1-
\sqrt{e^2\,a^2+1}\right)}\over{2}}+{{\log \left(\sqrt{a^2+1}+1
\right)}\over{2}}-{{\log \left(1-\sqrt{a^2+1}\right)}\over{2}}+
\sqrt{e^2\,a^2+1}-\sqrt{a^2+1}$$
=
=
/ / ________\ / ___________\ / ___________\ / ________\ | ___________ | / 2 | | / 2 2 | ________ | / 2 2 | | / 2 | | / 2 2 log\1 + \/ 1 + a / log\-1 + \/ 1 + a *e / / 2 log\1 + \/ 1 + a *e / log\-1 + \/ 1 + a / <\/ 1 + a *e + -------------------- + ------------------------ - \/ 1 + a - ----------------------- - --------------------- for And(a > -oo, a < oo, a != 0) | 2 2 2 2 | \ 1 otherwise
$$\begin{cases} - \sqrt{a^{2} + 1} + \sqrt{a^{2} e^{2} + 1} - \frac{\log{\left(\sqrt{a^{2} + 1} - 1 \right)}}{2} + \frac{\log{\left(\sqrt{a^{2} + 1} + 1 \right)}}{2} + \frac{\log{\left(\sqrt{a^{2} e^{2} + 1} - 1 \right)}}{2} - \frac{\log{\left(\sqrt{a^{2} e^{2} + 1} + 1 \right)}}{2} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\1 & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.