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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of 2*x
- Integral of sin(x+y)
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Integral of cos(y)^(-2)
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Integral of xexp(-x^2)
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Identical expressions
- sqrt(one +e^(two *x))
- square root of (1 plus e to the power of (2 multiply by x))
- square root of (one plus e to the power of (two multiply by x))
- √(1+e^(2*x))
- sqrt(1+e(2*x))
- sqrt1+e2*x
- sqrt(1+e^(2x))
- sqrt(1+e(2x))
- sqrt1+e2x
- sqrt1+e^2x
- sqrt(1+e^(2*x))dx
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Similar expressions
- sqrt(1-e^(2*x))
Integral of sqrt(1+e^(2*x)) dx
The solution
You have entered
[src]
1 / | | __________ | / 2*x | \/ 1 + e dx | / 0
$$\int\limits_{0}^{1} \sqrt{e^{2 x} + 1}\, dx$$
Integral(sqrt(1 + E^(2*x)), (x, 0, 1))
The answer (Indefinite)
[src]
$$-{{\log \left(\sqrt{e^{2\,x}+1}+1\right)}\over{2}}+{{\log \left(
\sqrt{e^{2\,x}+1}-1\right)}\over{2}}+\sqrt{e^{2\,x}+1}$$
The graph
The answer
[src]
/ ________\ / ________\
________ / ___\ | / 2 | | / 2 | / ___\
/ 2 log\1 + \/ 2 / log\-1 + \/ 1 + e / ___ log\1 + \/ 1 + e / log\-1 + \/ 2 /
\/ 1 + e + -------------- + --------------------- - \/ 2 - -------------------- - ---------------
2 2 2 2
$$-{{\log \left(\sqrt{e^2+1}+1\right)}\over{2}}+{{\log \left(1-\sqrt{
e^2+1}\right)}\over{2}}+{{\log \left(\sqrt{2}+1\right)}\over{2}}-{{
\log \left(1-\sqrt{2}\right)}\over{2}}+\sqrt{e^2+1}-\sqrt{2}$$
=
=
/ ________\ / ________\
________ / ___\ | / 2 | | / 2 | / ___\
/ 2 log\1 + \/ 2 / log\-1 + \/ 1 + e / ___ log\1 + \/ 1 + e / log\-1 + \/ 2 /
\/ 1 + e + -------------- + --------------------- - \/ 2 - -------------------- - ---------------
2 2 2 2
$$- \sqrt{2} - \frac{\log{\left(1 + \sqrt{1 + e^{2}} \right)}}{2} + \frac{\log{\left(-1 + \sqrt{1 + e^{2}} \right)}}{2} + \frac{\log{\left(1 + \sqrt{2} \right)}}{2} - \frac{\log{\left(-1 + \sqrt{2} \right)}}{2} + \sqrt{1 + e^{2}}$$
The graph
Use the examples entering the upper and lower limits of integration.