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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of (2x+3)
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Integral of 1-7*x^2
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Integral of (x+2)/(x(x-3))
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Integral of x/(2*x+1)
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Identical expressions
- one /(xsqrt(x- sixteen))
- 1 divide by (x square root of (x minus 16))
- one divide by (x square root of (x minus sixteen))
- 1/(x√(x-16))
- 1/xsqrtx-16
- 1 divide by (xsqrt(x-16))
- 1/(xsqrt(x-16))dx
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Similar expressions
- 1/(xsqrt(x+16))
Integral of 1/(xsqrt(x-16)) dx
The solution
You have entered
[src]
1 / | | 1 | ------------ dx | ________ | x*\/ x - 16 | / 0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{x - 16}}\, dx$$
Integral(1/(x*sqrt(x - 16)), (x, 0, 1))
The answer (Indefinite)
[src]
// / 4 \ \
||I*acosh|-----| |
|| | ___| |
/ || \\/ x / 16 |
| ||-------------- for --- > 1|
| 1 || 2 |x| |
| ------------ dx = C + |< |
| ________ || / 4 \ |
| x*\/ x - 16 ||-asin|-----| |
| || | ___| |
/ || \\/ x / |
||------------- otherwise |
\\ 2 /
$$\int \frac{1}{x \sqrt{x - 16}}\, dx = C + \begin{cases} \frac{i \operatorname{acosh}{\left(\frac{4}{\sqrt{x}} \right)}}{2} & \text{for}\: \frac{16}{\left|{x}\right|} > 1 \\- \frac{\operatorname{asin}{\left(\frac{4}{\sqrt{x}} \right)}}{2} & \text{otherwise} \end{cases}$$
The graph
The answer
[src]
I*acosh(4)
-oo*I + ----------
2
$$- \infty i + \frac{i \operatorname{acosh}{\left(4 \right)}}{2}$$
=
=
I*acosh(4)
-oo*I + ----------
2
$$- \infty i + \frac{i \operatorname{acosh}{\left(4 \right)}}{2}$$
-oo*i + i*acosh(4)/2
Use the examples entering the upper and lower limits of integration.