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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of (-1+u)/(1+u^2)
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Integral of cos2xsinx
- Integral of √(1-cos(x))
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Integral of 1/(1+x^(1/2))
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Identical expressions
- one /x(sqrt(x+ three))
- 1 divide by x( square root of (x plus 3))
- one divide by x( square root of (x plus three))
- 1/x(√(x+3))
- 1/xsqrtx+3
- 1 divide by x(sqrt(x+3))
- 1/x(sqrt(x+3))dx
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Similar expressions
- 1/x(sqrt(x-3))
Integral of 1/x(sqrt(x+3)) dx
The solution
You have entered
[src]
1 / | | _______ | \/ x + 3 | --------- dx | x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x + 3}}{x}\, dx$$
Integral(sqrt(x + 3)/x, (x, 0, 1))
The answer (Indefinite)
[src]
// / ___ _______\ \
|| ___ |\/ 3 *\/ 3 + x | |
/ ||-\/ 3 *acoth|---------------| |
| || \ 3 / |
| _______ ||------------------------------ for 3 + x > 3|
| \/ x + 3 _______ || 3 |
| --------- dx = C + 2*\/ 3 + x + 6*|< |
| x || / ___ _______\ |
| || ___ |\/ 3 *\/ 3 + x | |
/ ||-\/ 3 *atanh|---------------| |
|| \ 3 / |
||------------------------------ for 3 + x < 3|
\\ 3 /
$$\int \frac{\sqrt{x + 3}}{x}\, dx = C + 2 \sqrt{x + 3} + 6 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \sqrt{x + 3}}{3} \right)}}{3} & \text{for}\: x + 3 > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \sqrt{x + 3}}{3} \right)}}{3} & \text{for}\: x + 3 < 3 \end{cases}\right)$$
The graph
The answer
[src]
/ ___\
___ |2*\/ 3 |
oo - 2*\/ 3 *acoth|-------|
\ 3 /
$$- 2 \sqrt{3} \operatorname{acoth}{\left(\frac{2 \sqrt{3}}{3} \right)} + \infty$$
=
=
/ ___\
___ |2*\/ 3 |
oo - 2*\/ 3 *acoth|-------|
\ 3 /
$$- 2 \sqrt{3} \operatorname{acoth}{\left(\frac{2 \sqrt{3}}{3} \right)} + \infty$$
oo - 2*sqrt(3)*acoth(2*sqrt(3)/3)
Use the examples entering the upper and lower limits of integration.