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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 2*x/(-1+x)
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Integral of (x+1)/(x^2+2x-1)
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Integral of sin(5x)cos(x)
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Integral of sin(3x)*cos(4x)
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Identical expressions
- one /(xsqrt(one +x^ two))
- 1 divide by (x square root of (1 plus x squared ))
- one divide by (x square root of (one plus x to the power of two))
- 1/(x√(1+x^2))
- 1/(xsqrt(1+x2))
- 1/xsqrt1+x2
- 1/(xsqrt(1+x²))
- 1/(xsqrt(1+x to the power of 2))
- 1/xsqrt1+x^2
- 1 divide by (xsqrt(1+x^2))
- 1/(xsqrt(1+x^2))dx
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Similar expressions
- 1/(xsqrt(1-x^2))
Integral of 1/(xsqrt(1+x^2)) dx
The solution
You have entered
[src]
oo / | | 1 | ------------- dx | ________ | / 2 | x*\/ 1 + x | / 1
$$\int\limits_{1}^{\infty} \frac{1}{x \sqrt{x^{2} + 1}}\, dx$$
Integral(1/(x*sqrt(1 + x^2)), (x, 1, oo))
The answer (Indefinite)
[src]
/ | | 1 /1\ | ------------- dx = C - asinh|-| | ________ \x/ | / 2 | x*\/ 1 + x | /
$$\int \frac{1}{x \sqrt{x^{2} + 1}}\, dx = C - \operatorname{asinh}{\left(\frac{1}{x} \right)}$$
The graph
The answer
[src]
/ ___\ log\1 + \/ 2 /
$$\log{\left(1 + \sqrt{2} \right)}$$
=
=
/ ___\ log\1 + \/ 2 /
$$\log{\left(1 + \sqrt{2} \right)}$$
log(1 + sqrt(2))
Use the examples entering the upper and lower limits of integration.