Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^4lnx
Integral of -xe^x
Integral of x*dx/(x^2-1)
Integral of x^2/sqrt(x)
Identical expressions
(x^ two)/sqrt((x- three)(five -x))
(x squared ) divide by square root of ((x minus 3)(5 minus x))
(x to the power of two) divide by square root of ((x minus three)(five minus x))
(x^2)/√((x-3)(5-x))
(x2)/sqrt((x-3)(5-x))
x2/sqrtx-35-x
(x²)/sqrt((x-3)(5-x))
(x to the power of 2)/sqrt((x-3)(5-x))
x^2/sqrtx-35-x
(x^2) divide by sqrt((x-3)(5-x))
(x^2)/sqrt((x-3)(5-x))dx
Similar expressions
(x^2)/sqrt((x-3)(5+x))
(x^2)/sqrt((x+3)(5-x))

Solving integrals/ (x^2)/sqrt((x-3)(5-x))

Integral of (x^2)/sqrt((x-3)(5-x)) dx

The solution

You have entered [src]

  5                       
  /                       
 |                        
 |            2           
 |           x            
 |  ------------------- dx
 |    _________________   
 |  \/ (x - 3)*(5 - x)    
 |                        
/                         
3

$$\int\limits_{3}^{5} \frac{x^{2}}{\sqrt{\left(5 - x\right) \left(x - 3\right)}}\, dx$$

Integral(x^2/(sqrt((x - 1*3)*(5 - x))), (x, 3, 5))

Detail solution

Rewrite the integrand:

$\frac{x^{2}}{\sqrt{\left(5 - x\right) \left(x - 3\right)}} = \frac{x^{2}}{\sqrt{- x^{2} + 8 x - 15}}$

SqrtQuadraticDenomRule(a=-15, b=8, c=-1, coeffs=[1, 0, 0], context=x**2/sqrt(-x**2 + 8*x - 15), symbol=x)
Now simplify:

$- \frac{\left(x + 12\right) \sqrt{- x^{2} + 8 x - 15}}{2} + \frac{33 \operatorname{asin}{\left(x - 4 \right)}}{2}$
Add the constant of integration:

$- \frac{\left(x + 12\right) \sqrt{- x^{2} + 8 x - 15}}{2} + \frac{33 \operatorname{asin}{\left(x - 4 \right)}}{2}+ \mathrm{constant}$

The answer is:

$- \frac{\left(x + 12\right) \sqrt{- x^{2} + 8 x - 15}}{2} + \frac{33 \operatorname{asin}{\left(x - 4 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                           
 |                                                                            
 |           2                                       ________________         
 |          x                   33*asin(-4 + x)     /        2        /     x\
 | ------------------- dx = C + --------------- + \/  -15 - x  + 8*x *|-6 - -|
 |   _________________                 2                              \     2/
 | \/ (x - 3)*(5 - x)                                                         
 |                                                                            
/

$$-{{x\,\sqrt{-x^2+8\,x-15}}\over{2}}-6\,\sqrt{-x^2+8\,x-15}-{{33\, \arcsin \left({{8-2\,x}\over{2}}\right)}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

33*pi
-----
  2

$${{33\,\pi}\over{2}}$$

33*pi
-----
  2

$$\frac{33 \pi}{2}$$

Упростить

Numerical answer [src]

51.8362787661904

51.8362787661904

The graph

Use the examples entering the upper and lower limits of integration.

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (x^2)/sqrt((x-3)(5-x)) dx

Limits of integration:

The graph:

Piecewise:

The solution