Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of 1/5x
-
Integral of x*dx/(x^2+1)
-
Integral of x^3*exp(x^2)
- Integral of x^2*a^x
- Graphing y =:
- lnx/sqrtx
-
Identical expressions
- lnx/sqrtx
- lnx divide by square root of x
- lnx/√x
- lnx divide by sqrtx
- lnx/sqrtxdx
-
Similar expressions
- abs(sin(lnx)/sqrt(x))
- (x*ln(x))/(sqrt((x^2-1)^3))
- ln(x)/sqrt(x^3+3)
- (x^2+ln(x))/(sqrt(x^5-1))
- (x^2+lnx)/sqrt(x^5-1)
Integral of lnx/sqrtx dx
The solution
You have entered
[src]
1 / | | log(x) | ------ dx | ___ | \/ x | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{\sqrt{x}}\, dx$$
Integral(log(x)/(sqrt(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | log(x) ___ ___ | ------ dx = C - 4*\/ x + 2*\/ x *log(x) | ___ | \/ x | /
$$\int \frac{\log{\left(x \right)}}{\sqrt{x}}\, dx = C + 2 \sqrt{x} \log{\left(x \right)} - 4 \sqrt{x}$$
The answer
[src]
1 / | | / 2*log(x) /1 \ | | -------- for And|- < 1, x < 1| | | ___ \x / | | \/ x | | | | log(x) /1 \ | | ------ for Or|- < 1, x < 1| | | ___ \x / | < \/ x dx | | | | __0, 3 /3/2, 3/2, 1 | \ | |/__ | | x| | |\_|3, 3 \ 1/2, 1/2, 0 | / __0, 3 /1/2, 3/2, 1 | \ __2, 1 / 0 3/2, 3/2 | \ | |-------------------------------------- + /__ | | x| /__ | | x| | | 2 \_|3, 3 \ 1/2, 1/2, 0 | / \_|3, 3 \1/2, 1/2 0 | / | |------------------------------------------------------------------------------- - -------------------------------- otherwise | \ x x | / 0
$$\int\limits_{0}^{1} \begin{cases} \frac{2 \log{\left(x \right)}}{\sqrt{x}} & \text{for}\: \frac{1}{x} < 1 \wedge x < 1 \\\frac{\log{\left(x \right)}}{\sqrt{x}} & \text{for}\: \frac{1}{x} < 1 \vee x < 1 \\\frac{{G_{3, 3}^{0, 3}\left(\begin{matrix} \frac{1}{2}, \frac{3}{2}, 1 & \\ & \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {x} \right)} + \frac{{G_{3, 3}^{0, 3}\left(\begin{matrix} \frac{3}{2}, \frac{3}{2}, 1 & \\ & \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {x} \right)}}{2}}{x} - \frac{{G_{3, 3}^{2, 1}\left(\begin{matrix} 0 & \frac{3}{2}, \frac{3}{2} \\\frac{1}{2}, \frac{1}{2} & 0 \end{matrix} \middle| {x} \right)}}{x} & \text{otherwise} \end{cases}\, dx$$
=
=
1 / | | / 2*log(x) /1 \ | | -------- for And|- < 1, x < 1| | | ___ \x / | | \/ x | | | | log(x) /1 \ | | ------ for Or|- < 1, x < 1| | | ___ \x / | < \/ x dx | | | | __0, 3 /3/2, 3/2, 1 | \ | |/__ | | x| | |\_|3, 3 \ 1/2, 1/2, 0 | / __0, 3 /1/2, 3/2, 1 | \ __2, 1 / 0 3/2, 3/2 | \ | |-------------------------------------- + /__ | | x| /__ | | x| | | 2 \_|3, 3 \ 1/2, 1/2, 0 | / \_|3, 3 \1/2, 1/2 0 | / | |------------------------------------------------------------------------------- - -------------------------------- otherwise | \ x x | / 0
$$\int\limits_{0}^{1} \begin{cases} \frac{2 \log{\left(x \right)}}{\sqrt{x}} & \text{for}\: \frac{1}{x} < 1 \wedge x < 1 \\\frac{\log{\left(x \right)}}{\sqrt{x}} & \text{for}\: \frac{1}{x} < 1 \vee x < 1 \\\frac{{G_{3, 3}^{0, 3}\left(\begin{matrix} \frac{1}{2}, \frac{3}{2}, 1 & \\ & \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {x} \right)} + \frac{{G_{3, 3}^{0, 3}\left(\begin{matrix} \frac{3}{2}, \frac{3}{2}, 1 & \\ & \frac{1}{2}, \frac{1}{2}, 0 \end{matrix} \middle| {x} \right)}}{2}}{x} - \frac{{G_{3, 3}^{2, 1}\left(\begin{matrix} 0 & \frac{3}{2}, \frac{3}{2} \\\frac{1}{2}, \frac{1}{2} & 0 \end{matrix} \middle| {x} \right)}}{x} & \text{otherwise} \end{cases}\, dx$$
Use the examples entering the upper and lower limits of integration.