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 x*x
-
Integral of e^(x*(-3))
-
Integral of sin²xcos²x
-
Integral of (x+2)dx
-
Identical expressions
- (kx^(- one)+c)^(- one / two)
- (kx to the power of ( minus 1) plus c) to the power of ( minus 1 divide by 2)
- (kx to the power of ( minus one) plus c) to the power of ( minus one divide by two)
- (kx(-1)+c)(-1/2)
- kx-1+c-1/2
- kx^-1+c^-1/2
- (kx^(-1)+c)^(-1 divide by 2)
- (kx^(-1)+c)^(-1/2)dx
-
Similar expressions
- (kx^(1)+c)^(-1/2)
- (kx^(-1)+c)^(1/2)
- (kx^(-1)-c)^(-1/2)
Integral of (kx^(-1)+c)^(-1/2) dx
The solution
You have entered
[src]
1 / | | 1 | ----------- dx | _______ | / k | / - + c | \/ x | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{c + \frac{k}{x}}}\, dx$$
The answer (Indefinite)
[src]
/ ___ ___\
|\/ c *\/ x | _________
/ k*asinh|-----------| ___ ___ / c*x
| | ___ | \/ k *\/ x * / 1 + ---
| 1 \ \/ k / \/ k
| ----------- dx = C - -------------------- + -------------------------
| _______ 3/2 c
| / k c
| / - + c
| \/ x
|
/
$$\int \frac{1}{\sqrt{c + \frac{k}{x}}}\, dx = \frac{\sqrt{k} \sqrt{x} \sqrt{\frac{c x}{k} + 1}}{c} + C - \frac{k \operatorname{asinh}{\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{k}} \right)}}{c^{\frac{3}{2}}}$$
The answer
[src]
/ ___\
_______ |\/ c |
___ / c k*asinh|-----|
\/ k * / 1 + - | ___|
\/ k \\/ k /
----------------- - --------------
c 3/2
c
$$\frac{\sqrt{k} \sqrt{\frac{c}{k} + 1}}{c} - \frac{k \operatorname{asinh}{\left(\frac{\sqrt{c}}{\sqrt{k}} \right)}}{c^{\frac{3}{2}}}$$
=
=
/ ___\
_______ |\/ c |
___ / c k*asinh|-----|
\/ k * / 1 + - | ___|
\/ k \\/ k /
----------------- - --------------
c 3/2
c
$$\frac{\sqrt{k} \sqrt{\frac{c}{k} + 1}}{c} - \frac{k \operatorname{asinh}{\left(\frac{\sqrt{c}}{\sqrt{k}} \right)}}{c^{\frac{3}{2}}}$$
Use the examples entering the upper and lower limits of integration.