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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 (x^2-x+1)/(x^2+x+1)^2
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Integral of x/(1+sqrt(x))
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Integral of x/(1+3*x^2)
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Integral of tan^3xdx
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Identical expressions
- (x- one)^(one / two)/x
- (x minus 1) to the power of (1 divide by 2) divide by x
- (x minus 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
You have entered
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5 / | | _______ | \/ x - 1 | --------- dx | x | / 1
$$\int\limits_{1}^{5} \frac{\sqrt{x - 1}}{x}\, dx$$
Integral(sqrt(x - 1)/x, (x, 1, 5))
The answer (Indefinite)
[src]
/ | | _______ | \/ x - 1 / ________\ ________ | --------- dx = C - 2*atan\\/ -1 + x / + 2*\/ -1 + x | x | /
$$\int \frac{\sqrt{x - 1}}{x}\, dx = C + 2 \sqrt{x - 1} - 2 \operatorname{atan}{\left(\sqrt{x - 1} \right)}$$
The graph
The answer
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/ ___\
|\/ 5 |
4 - pi + 2*asin|-----|
\ 5 /
$$- \pi + 2 \operatorname{asin}{\left(\frac{\sqrt{5}}{5} \right)} + 4$$
=
=
/ ___\
|\/ 5 |
4 - pi + 2*asin|-----|
\ 5 /
$$- \pi + 2 \operatorname{asin}{\left(\frac{\sqrt{5}}{5} \right)} + 4$$
4 - pi + 2*asin(sqrt(5)/5)
The graph
Use the examples entering the upper and lower limits of integration.