### Browsed byCategory: How to

Complete the square solver

## Complete the square solver

Input interpretation
complete the square | 28 + 10 x + x^2
Result
(x + 5)^2 + 3
Geometric figure
parabola
Polynomial discriminant
Delta = -12
Derivative
d/dx((x + 5)^2 + 3) = 2 (x + 5)
Indefinite integral
integral (3 + (5 + x)^2) dx = x^3/3 + 5 x^2 + 28 x + constant
Global minimum
min{(x + 5)^2 + 3} = 3 at x = -5
Evaluate the double integral

## Evaluate the double integral

Indefinite integral
integral integral (x^2 + y^2) dy dx = c_1 y + c_2 + (x^3 y)/3 + (x y^3)/3
Definite integral over a disk of radius R
integral integral_(x^2 + y^2
Double integral solver

## Double integral solver

Indefinite integral
integral integral (x^2 + y^2) dy dx = c_1 y + c_2 + (x^3 y)/3 + (x y^3)/3
Definite integral over a disk of radius R
integral integral_(x^2 + y^2
Partial fraction solver

## Partial fraction solver

Input
partial fractions | 1/((1 + x) (5 + x))
Result
1/((x + 1) (x + 5)) = 1/(4 (x + 1)) – 1/(4 (x + 5))
Partial fraction decomposition solver

## Partial fraction decomposition solver

Input
partial fractions | 1/((1 + x) (5 + x))
Result
1/((x + 1) (x + 5)) = 1/(4 (x + 1)) – 1/(4 (x + 5))
A union b complement

## A union b complement

Input
a Union[b Complement]
Result
a b Complement
A complement union b complement

## A complement union b complement

Input
a Complement Union[b Complement]
Result
a b Complement^2
Sum and product

## Sum and product

Input interpretation
Algebra > Sums | Algebra > Products
Product sum

## Product sum

Input interpretation
Algebra > Products | Algebra > Sums
Chemistry problem solver

## Chemistry problem solver

Input interpretation
famous chemistry problems | provers
Summary
August Kroenig | Rudolf Clausius
(based on 1 values; 21 unavailable)
Basic information
| Rudolf Clausius
full name | Rudolf Julius Emmanuel Clausius
date of birth | Wednesday, January 2, 1822 (195 years ago)
place of birth | Koszalin, Zachodniopomorskie, Poland
date of death | Friday, August 24, 1888 (age: 66 years)
(128 years ago)
place of death | Bonn, North Rhine-Westphalia, Germany
Table
ideal gas law | Rudolf Clausius | August Kroenig