👉 Try now NerdPal! Our new math app on iOS and Android
  1. calculators
  2. Gaussian Elimination

Gaussian Elimination Calculator

Get detailed solutions to your math problems with our Gaussian Elimination step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

1

Solved example of matrices

$\int\frac{1}{x\left(x+1\right)}dx$
2

Rewrite the fraction $\frac{1}{x\left(x+1\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{1}{x\left(x+1\right)}=\frac{A}{x}+\frac{B}{x+1}$
3

Find the values for the unknown coefficients: $A, B$. The first step is to multiply both sides of the equation from the previous step by $x\left(x+1\right)$

$1=x\left(x+1\right)\left(\frac{A}{x}+\frac{B}{x+1}\right)$

4

Multiplying polynomials

$1=\frac{x\left(x+1\right)A}{x}+\frac{x\left(x+1\right)B}{x+1}$
5

Simplifying

$1=\left(x+1\right)A+xB$
6

Assigning values to $x$ we obtain the following system of equations

$\begin{matrix}1=A&\:\:\:\:\:\:\:(x=0) \\ 1=-B&\:\:\:\:\:\:\:(x=-1)\end{matrix}$
7

Proceed to solve the system of linear equations

$\begin{matrix}1A & + & 0B & =1 \\ 0A & - & 1B & =1\end{matrix}$
8

Rewrite as a coefficient matrix

$\left(\begin{matrix}1 & 0 & 1 \\ 0 & -1 & 1\end{matrix}\right)$
9

Reducing the original matrix to a identity matrix using Gaussian Elimination

$\left(\begin{matrix}1 & 0 & 1 \\ 0 & 1 & -1\end{matrix}\right)$
10

The integral of $\frac{1}{x\left(x+1\right)}$ in decomposed fraction equals

$\int\left(\frac{1}{x}+\frac{-1}{x+1}\right)dx$
11

Expand the integral $\int\left(\frac{1}{x}+\frac{-1}{x+1}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int\frac{1}{x}dx+\int\frac{-1}{x+1}dx$

The integral of the inverse of the lineal function is given by the following formula, $\displaystyle\int\frac{1}{x}dx=\ln(x)$

$\ln\left(x\right)$
12

The integral $\int\frac{1}{x}dx$ results in: $\ln\left(x\right)$

$\ln\left(x\right)$

The integral of a function times a constant ($-1$) is equal to the constant times the integral of the function

$-\int\frac{1}{1+x}dx$

Apply the formula: $\int\frac{n}{x+b}dx$$=nsign\left(x\right)\ln\left(x+b\right)+C$, where $b=1$ and $n=1$

$-\ln\left(x+1\right)$
13

The integral $\int\frac{-1}{x+1}dx$ results in: $-\ln\left(x+1\right)$

$-\ln\left(x+1\right)$
14

Gather the results of all integrals

$\ln\left(x\right)-\ln\left(x+1\right)$
15

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\ln\left(x\right)-\ln\left(x+1\right)+C_0$

Final Answer

$\ln\left(x\right)-\ln\left(x+1\right)+C_0$

Struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!