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How to use it?
- Integral of d{x}:
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Integral of e^(3x)
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Integral of x*exp(-x)
- Integral of 1/sin^3x
- Integral of sin(x)/cos^2x+5cos(x)+6
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Identical expressions
- one /(x*sqrt(x)*sqrt(x+ one))
- 1 divide by (x multiply by square root of (x) multiply by square root of (x plus 1))
- one divide by (x multiply by square root of (x) multiply by square root of (x plus one))
- 1/(x*√(x)*√(x+1))
- 1/(xsqrt(x)sqrt(x+1))
- 1/xsqrtxsqrtx+1
- 1 divide by (x*sqrt(x)*sqrt(x+1))
- 1/(x*sqrt(x)*sqrt(x+1))dx
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Similar expressions
- 1/(x*sqrt(x)*sqrt(x-1))
Integral of 1/(x*sqrt(x)*sqrt(x+1)) dx
The solution
You have entered
[src]
1 / | | 1 | ----------------- dx | ___ _______ | x*\/ x *\/ x + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{x} x \sqrt{x + 1}}\, dx$$
Integral(1/((x*sqrt(x))*sqrt(x + 1)), (x, 0, 1))
The answer (Indefinite)
[src]
// 2*I 1 \
||---------------- for ------- > 1|
|| ____________ |1 + x| |
/ || / 1 |
| || / -1 + ----- |
| 1 ||\/ 1 + x |
| ----------------- dx = C + |< |
| ___ _______ || -2 |
| x*\/ x *\/ x + 1 ||--------------- otherwise |
| || ___________ |
/ || / 1 |
|| / 1 - ----- |
\\\/ 1 + x /
$$\int \frac{1}{\sqrt{x} x \sqrt{x + 1}}\, dx = C + \begin{cases} \frac{2 i}{\sqrt{-1 + \frac{1}{x + 1}}} & \text{for}\: \frac{1}{\left|{x + 1}\right|} > 1 \\- \frac{2}{\sqrt{1 - \frac{1}{x + 1}}} & \text{otherwise} \end{cases}$$
The graph
Use the examples entering the upper and lower limits of integration.