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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x*exp(x)
- Integral of sin(ln(x))/x
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Integral of (x+1)^(1/2)/x
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Integral of sin(3x)cos(x)
- Sum of series:
- (x+1)^(1/2)/x
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Identical expressions
- (x+ one)^(one / two)/x
- (x plus 1) to the power of (1 divide by 2) divide by x
- (x plus one) to the power of (one divide by two) divide by x
- (x+1)(1/2)/x
- x+11/2/x
- x+1^1/2/x
- (x+1)^(1 divide by 2) divide by x
- (x+1)^(1/2)/xdx
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Similar expressions
- (x-1)^(1/2)/x
Integral of (x+1)^(1/2)/x dx
The solution
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1 / | | _______ | \/ x + 1 | --------- dx | x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x + 1}}{x}\, dx$$
Integral(sqrt(x + 1)/x, (x, 0, 1))
The answer (Indefinite)
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/ | | _______ | \/ x + 1 / _______\ _______ / _______\ | --------- dx = C - log\1 + \/ 1 + x / + 2*\/ 1 + x + log\-1 + \/ 1 + x / | x | /
$$\int \frac{\sqrt{x + 1}}{x}\, dx = C + 2 \sqrt{x + 1} + \log{\left(\sqrt{x + 1} - 1 \right)} - \log{\left(\sqrt{x + 1} + 1 \right)}$$
The graph
The answer
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/ ___\ oo - 2*acoth\\/ 2 /
$$- 2 \operatorname{acoth}{\left(\sqrt{2} \right)} + \infty$$
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/ ___\ oo - 2*acoth\\/ 2 /
$$- 2 \operatorname{acoth}{\left(\sqrt{2} \right)} + \infty$$
oo - 2*acoth(sqrt(2))
The graph
Use the examples entering the upper and lower limits of integration.