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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
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- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x^(-2)
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Integral of sin(3x)
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Integral of logx
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Integral of x^2/(1+x)
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Identical expressions
- one /(x(sqrt(one +(sqrtx))))
- 1 divide by (x( square root of (1 plus ( square root of x))))
- one divide by (x( square root of (one plus ( square root of x))))
- 1/(x(√(1+(√x))))
- 1/xsqrt1+sqrtx
- 1 divide by (x(sqrt(1+(sqrtx))))
- 1/(x(sqrt(1+(sqrtx))))dx
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Similar expressions
- 1/(x(sqrt(1-(sqrtx))))
Integral of 1/(x(sqrt(1+(sqrtx)))) dx
The solution
You have entered
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1 / | | 1 | ---------------- dx | ___________ | / ___ | x*\/ 1 + \/ x | / 2
$$\int\limits_{2}^{1} \frac{1}{x \sqrt{\sqrt{x} + 1}}\, dx$$
Integral(1/(x*sqrt(1 + sqrt(x))), (x, 2, 1))
The answer (Indefinite)
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/ | | 1 / 1 \ | ---------------- dx = C - 4*asinh|-----| | ___________ |4 ___| | / ___ \\/ x / | x*\/ 1 + \/ x | /
$$\int \frac{1}{x \sqrt{\sqrt{x} + 1}}\, dx = C - 4 \operatorname{asinh}{\left(\frac{1}{\sqrt[4]{x}} \right)}$$
The graph
The answer
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/ 3/4\
/ ___\ |2 |
- 4*log\1 + \/ 2 / + 4*asinh|----|
\ 2 /
$$- 4 \log{\left(1 + \sqrt{2} \right)} + 4 \operatorname{asinh}{\left(\frac{2^{\frac{3}{4}}}{2} \right)}$$
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/ 3/4\
/ ___\ |2 |
- 4*log\1 + \/ 2 / + 4*asinh|----|
\ 2 /
$$- 4 \log{\left(1 + \sqrt{2} \right)} + 4 \operatorname{asinh}{\left(\frac{2^{\frac{3}{4}}}{2} \right)}$$
-4*log(1 + sqrt(2)) + 4*asinh(2^(3/4)/2)
Use the examples entering the upper and lower limits of integration.