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- 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}:
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Integral of e^-x
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Integral of e^x/x
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Integral of 1/sin²(x)
- Integral of sqrt(1+x)/sqrt(1-x)
- Derivative of:
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sqrt(1+x)/sqrt(1-x)
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Identical expressions
- sqrt(one +x)/sqrt(one -x)
- square root of (1 plus x) divide by square root of (1 minus x)
- square root of (one plus x) divide by square root of (one minus x)
- √(1+x)/√(1-x)
- sqrt1+x/sqrt1-x
- sqrt(1+x) divide by sqrt(1-x)
- sqrt(1+x)/sqrt(1-x)dx
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Similar expressions
- sqrt(1+x)/sqrt(1+x)
- sqrt(1-x)/sqrt(1-x)
- (sqrt(1+x))/(sqrt(1-x))
Integral of sqrt(1+x)/sqrt(1-x) dx
The solution
You have entered
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1 / | | _______ | \/ 1 + x | --------- dx | _______ | \/ 1 - x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x + 1}}{\sqrt{1 - x}}\, dx$$
Integral(sqrt(1 + x)/sqrt(1 - x), (x, 0, 1))
The answer (Indefinite)
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/ | | _______ // _______ _______ / ___ _______\ \ | \/ 1 + x || \/ 1 + x *\/ 1 - x |\/ 2 *\/ 1 + x | | | --------- dx = C + 2*|<- ------------------- + asin|---------------| for And(x >= -1, x < 1)| | _______ || 2 \ 2 / | | \/ 1 - x \\ / | /
$$\int \frac{\sqrt{x + 1}}{\sqrt{1 - x}}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{1 - x} \sqrt{x + 1}}{2} + \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} & \text{for}\: x \geq -1 \wedge x < 1 \end{cases}\right)$$
The graph
Use the examples entering the upper and lower limits of integration.