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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*cos(x/2)
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Integral of x*dx/(x^2-1)
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Integral of x^5/(x^2+1)
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Integral of x/(2*x+1)
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Identical expressions
- (one)/(x*sqrt(x- eleven))
- (1) divide by (x multiply by square root of (x minus 11))
- (one) divide by (x multiply by square root of (x minus eleven))
- (1)/(x*√(x-11))
- (1)/(xsqrt(x-11))
- 1/xsqrtx-11
- (1) divide by (x*sqrt(x-11))
- (1)/(x*sqrt(x-11))dx
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Similar expressions
- (1)/(x*sqrt(x+11))
Integral of (1)/(x*sqrt(x-11)) dx
The solution
You have entered
[src]
1 / | | 1 | ------------ dx | ________ | x*\/ x - 11 | / 0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{x - 11}}\, dx$$
Integral(1/(x*sqrt(x - 11)), (x, 0, 1))
The answer (Indefinite)
[src]
// / ____\ \
|| ____ |\/ 11 | |
||2*I*\/ 11 *acosh|------| |
|| | ___ | |
/ || \\/ x / 11 |
| ||------------------------ for --- > 1|
| 1 || 11 |x| |
| ------------ dx = C + |< |
| ________ || / ____\ |
| x*\/ x - 11 || ____ |\/ 11 | |
| || -2*\/ 11 *asin|------| |
/ || | ___ | |
|| \\/ x / |
|| ---------------------- otherwise |
\\ 11 /
$$\int \frac{1}{x \sqrt{x - 11}}\, dx = C + \begin{cases} \frac{2 \sqrt{11} i \operatorname{acosh}{\left(\frac{\sqrt{11}}{\sqrt{x}} \right)}}{11} & \text{for}\: \frac{11}{\left|{x}\right|} > 1 \\- \frac{2 \sqrt{11} \operatorname{asin}{\left(\frac{\sqrt{11}}{\sqrt{x}} \right)}}{11} & \text{otherwise} \end{cases}$$
The graph
The answer
[src]
____ / ____\
2*I*\/ 11 *acosh\\/ 11 /
-oo*I + ------------------------
11
$$- \infty i + \frac{2 \sqrt{11} i \operatorname{acosh}{\left(\sqrt{11} \right)}}{11}$$
=
=
____ / ____\
2*I*\/ 11 *acosh\\/ 11 /
-oo*I + ------------------------
11
$$- \infty i + \frac{2 \sqrt{11} i \operatorname{acosh}{\left(\sqrt{11} \right)}}{11}$$
-oo*i + 2*i*sqrt(11)*acosh(sqrt(11))/11
Use the examples entering the upper and lower limits of integration.