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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^(-1/2)
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Integral of 1/sqrt(1+u^2)
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Integral of x^4lnx
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Integral of x*dx/(x^2-1)
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Identical expressions
- sqrt(x+ three)/((two *x))
- square root of (x plus 3) divide by ((2 multiply by x))
- square root of (x plus three) divide by ((two multiply by x))
- √(x+3)/((2*x))
- sqrt(x+3)/((2x))
- sqrtx+3/2x
- sqrt(x+3) divide by ((2*x))
- sqrt(x+3)/((2*x))dx
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Similar expressions
- sqrt(x-3)/((2*x))
Integral of sqrt(x+3)/((2*x)) dx
The solution
You have entered
[src]
6 / | | _______ | \/ x + 3 | --------- dx | 2*x | / 1
$$\int\limits_{1}^{6} \frac{\sqrt{x + 3}}{2 x}\, dx$$
Integral(sqrt(x + 3)/((2*x)), (x, 1, 6))
The answer (Indefinite)
[src]
// / ___ _______\ \
|| ___ |\/ 3 *\/ x + 3 | |
/ ||-\/ 3 *acoth|---------------| |
| || \ 3 / |
| _______ ||------------------------------ for x + 3 > 3|
| \/ x + 3 _______ || 3 |
| --------- dx = C + \/ x + 3 + 3*|< |
| 2*x || / ___ _______\ |
| || ___ |\/ 3 *\/ x + 3 | |
/ ||-\/ 3 *atanh|---------------| |
|| \ 3 / |
||------------------------------ for x + 3 < 3|
\\ 3 /
$$\int \frac{\sqrt{x + 3}}{2 x}\, dx = C + \sqrt{x + 3} + 3 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \sqrt{x + 3}}{3} \right)}}{3} & \text{for}\: x + 3 > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \sqrt{x + 3}}{3} \right)}}{3} & \text{for}\: x + 3 < 3 \end{cases}\right)$$
The graph
The answer
[src]
/ ___\
___ |2*\/ 3 | ___ / ___\
1 + \/ 3 *acoth|-------| - \/ 3 *acoth\\/ 3 /
\ 3 /
$$- \sqrt{3} \operatorname{acoth}{\left(\sqrt{3} \right)} + 1 + \sqrt{3} \operatorname{acoth}{\left(\frac{2 \sqrt{3}}{3} \right)}$$
=
=
/ ___\
___ |2*\/ 3 | ___ / ___\
1 + \/ 3 *acoth|-------| - \/ 3 *acoth\\/ 3 /
\ 3 /
$$- \sqrt{3} \operatorname{acoth}{\left(\sqrt{3} \right)} + 1 + \sqrt{3} \operatorname{acoth}{\left(\frac{2 \sqrt{3}}{3} \right)}$$
1 + sqrt(3)*acoth(2*sqrt(3)/3) - sqrt(3)*acoth(sqrt(3))
Use the examples entering the upper and lower limits of integration.