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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 x^(2/3)*dx
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Integral of x/(sinx^2)^2
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Integral of x*ln(x^2+1)
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Integral of e^xsin(x/2)
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Identical expressions
- (sqrt(x+ two))/(x- one)
- ( square root of (x plus 2)) divide by (x minus 1)
- ( square root of (x plus two)) divide by (x minus one)
- (√(x+2))/(x-1)
- sqrtx+2/x-1
- (sqrt(x+2)) divide by (x-1)
- (sqrt(x+2))/(x-1)dx
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Similar expressions
- sqrt((x+2)/(x-1))*(1)/(x+2)^2
- (sqrt(x-2))/(x-1)
- (sqrt(x+2))/(x+1)
Integral of (sqrt(x+2))/(x-1) dx
The solution
You have entered
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1 / | | _______ | \/ x + 2 | --------- dx | x - 1 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x + 2}}{x - 1}\, dx$$
Integral(sqrt(x + 2)/(x - 1), (x, 0, 1))
The answer (Indefinite)
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// / ___ _______\ \
|| ___ |\/ 3 *\/ 2 + x | |
/ ||-\/ 3 *acoth|---------------| |
| || \ 3 / |
| _______ ||------------------------------ for 2 + x > 3|
| \/ x + 2 _______ || 3 |
| --------- dx = C + 2*\/ 2 + x + 6*|< |
| x - 1 || / ___ _______\ |
| || ___ |\/ 3 *\/ 2 + x | |
/ ||-\/ 3 *atanh|---------------| |
|| \ 3 / |
||------------------------------ for 2 + x < 3|
\\ 3 /
$$\int \frac{\sqrt{x + 2}}{x - 1}\, dx = C + 2 \sqrt{x + 2} + 6 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \sqrt{x + 2}}{3} \right)}}{3} & \text{for}\: x + 2 > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \sqrt{x + 2}}{3} \right)}}{3} & \text{for}\: x + 2 < 3 \end{cases}\right)$$
The graph
The answer
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/ ___\
___ |\/ 6 |
-oo + 2*\/ 3 *atanh|-----|
\ 3 /
$$-\infty + 2 \sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{6}}{3} \right)}$$
=
=
/ ___\
___ |\/ 6 |
-oo + 2*\/ 3 *atanh|-----|
\ 3 /
$$-\infty + 2 \sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{6}}{3} \right)}$$
-oo + 2*sqrt(3)*atanh(sqrt(6)/3)
The graph
Use the examples entering the upper and lower limits of integration.