Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
- Integral of 1/tan(y)
- Integral of lnx²
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Integral of 1/(3cos^2x+4sin^2x)
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Integral of (5x^4-4x^3+3x^2-1)
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Identical expressions
- one /(u*(√(u^ two -a^ two)))
- 1 divide by (u multiply by (√(u squared minus a squared )))
- one divide by (u multiply by (√(u to the power of two minus a to the power of two)))
- 1/(u*(√(u2-a2)))
- 1/u*√u2-a2
- 1/(u*(√(u²-a²)))
- 1/(u*(√(u to the power of 2-a to the power of 2)))
- 1/(u(√(u^2-a^2)))
- 1/(u(√(u2-a2)))
- 1/u√u2-a2
- 1/u√u^2-a^2
- 1 divide by (u*(√(u^2-a^2)))
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Similar expressions
- 1/(u*(√(u^2+a^2)))
Integral of 1/(u*(√(u^2-a^2))) du
The solution
You have entered
[src]
1 / | | 1 | 1*-------------- du | _________ | / 2 2 | u*\/ u - a | / 0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{u \sqrt{- a^{2} + u^{2}}}\, du$$
The answer (Indefinite)
[src]
// /a\ \
||I*acosh|-| | 2| |
|| \u/ |a | |
/ ||---------- for |--| > 1|
| || a | 2| |
| 1 || |u | |
| 1*-------------- du = C + |< |
| _________ || /a\ |
| / 2 2 ||-asin|-| |
| u*\/ u - a || \u/ |
| ||--------- otherwise |
/ || a |
\\ /
$$\int 1 \cdot \frac{1}{u \sqrt{- a^{2} + u^{2}}}\, du = C + \begin{cases} \frac{i \operatorname{acosh}{\left(\frac{a}{u} \right)}}{a} & \text{for}\: \left|{\frac{a^{2}}{u^{2}}}\right| > 1 \\- \frac{\operatorname{asin}{\left(\frac{a}{u} \right)}}{a} & \text{otherwise} \end{cases}$$
The answer
[src]
1 / | | / | 2| | | -I |a | | |--------------------------- for ---- > 1 | | _______ ________ 2 | | 2 / a / a u | |u * / 1 + - * / -1 + - | | \/ u \/ u | | | < 1 du | | ----------------- otherwise | | ________ | | / 2 | | 2 / a | | u * / 1 - -- | | / 2 | | \/ u | \ | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i}{u^{2} \sqrt{\frac{a}{u} - 1} \sqrt{\frac{a}{u} + 1}} & \text{for}\: \frac{\left|{a^{2}}\right|}{u^{2}} > 1 \\\frac{1}{u^{2} \sqrt{- \frac{a^{2}}{u^{2}} + 1}} & \text{otherwise} \end{cases}\, du$$
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1 / | | / | 2| | | -I |a | | |--------------------------- for ---- > 1 | | _______ ________ 2 | | 2 / a / a u | |u * / 1 + - * / -1 + - | | \/ u \/ u | | | < 1 du | | ----------------- otherwise | | ________ | | / 2 | | 2 / a | | u * / 1 - -- | | / 2 | | \/ u | \ | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i}{u^{2} \sqrt{\frac{a}{u} - 1} \sqrt{\frac{a}{u} + 1}} & \text{for}\: \frac{\left|{a^{2}}\right|}{u^{2}} > 1 \\\frac{1}{u^{2} \sqrt{- \frac{a^{2}}{u^{2}} + 1}} & \text{otherwise} \end{cases}\, du$$
Use the examples entering the upper and lower limits of integration.