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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sqrt(16-x^2)/x
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Integral of sin⁴xcos²x
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Integral of 4x^3-2x^2
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Integral of cos(2x)*cos(7x)
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Identical expressions
- sqrt(sixteen -x^ two)/x
- square root of (16 minus x squared ) divide by x
- square root of (sixteen minus x to the power of two) divide by x
- √(16-x^2)/x
- sqrt(16-x2)/x
- sqrt16-x2/x
- sqrt(16-x²)/x
- sqrt(16-x to the power of 2)/x
- sqrt16-x^2/x
- sqrt(16-x^2) divide by x
- sqrt(16-x^2)/xdx
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Similar expressions
- sqrt(16+x^2)/x
Integral of sqrt(16-x^2)/x dx
The solution
You have entered
[src]
1 / | | _________ | / 2 | \/ 16 - x | ------------ dx | x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{16 - x^{2}}}{x}\, dx$$
Integral(sqrt(16 - x^2)/x, (x, 0, 1))
The answer (Indefinite)
[src]
// /4\ x 16 16 \
||- 4*acosh|-| - -------------- + ---------------- for ---- > 1|
/ || \x/ _________ _________ | 2| |
| || / 16 / 16 |x | |
| _________ || / -1 + -- x* / -1 + -- |
| / 2 || / 2 / 2 |
| \/ 16 - x || \/ x \/ x |
| ------------ dx = C + |< |
| x || /4\ I*x 16*I |
| || 4*I*asin|-| + ------------- - --------------- otherwise |
/ || \x/ ________ ________ |
|| / 16 / 16 |
|| / 1 - -- x* / 1 - -- |
|| / 2 / 2 |
\\ \/ x \/ x /
$$\int \frac{\sqrt{16 - x^{2}}}{x}\, dx = C + \begin{cases} - \frac{x}{\sqrt{-1 + \frac{16}{x^{2}}}} - 4 \operatorname{acosh}{\left(\frac{4}{x} \right)} + \frac{16}{x \sqrt{-1 + \frac{16}{x^{2}}}} & \text{for}\: \frac{16}{\left|{x^{2}}\right|} > 1 \\\frac{i x}{\sqrt{1 - \frac{16}{x^{2}}}} + 4 i \operatorname{asin}{\left(\frac{4}{x} \right)} - \frac{16 i}{x \sqrt{1 - \frac{16}{x^{2}}}} & \text{otherwise} \end{cases}$$
The graph
The answer
[src]
oo - 4*acosh(4)
$$- 4 \operatorname{acosh}{\left(4 \right)} + \infty$$
=
=
oo - 4*acosh(4)
$$- 4 \operatorname{acosh}{\left(4 \right)} + \infty$$
oo - 4*acosh(4)
The graph
Use the examples entering the upper and lower limits of integration.