Mister Exam

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Integral of d{x}:
Integral of 2/x^4
Integral of 1/(1+4x^2)
Integral of x^2*e^(x^3)
Integral of (x^2-1)e^x
Graphing y =:
x^2+8x+16
Derivative of:
x^2+8x+16
Identical expressions
x^ two +8x+ sixteen
x squared plus 8x plus 16
x to the power of two plus 8x plus sixteen
x2+8x+16
x²+8x+16
x to the power of 2+8x+16
x^2+8x+16dx
Similar expressions
x^2-8x+16
x^2+8x-16

Solving integrals/ x^2+8x+16

Integral of x^2+8x+16 dx

The solution

You have entered [src]

 -5                   
  /                   
 |                    
 |  / 2           \   
 |  \x  + 8*x + 16/ dx
 |                    
/                     
1

$$\int\limits_{1}^{-5} \left(\left(x^{2} + 8 x\right) + 16\right)\, dx$$

Integral(x^2 + 8*x + 16, (x, 1, -5))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 8 x\, dx = 8 \int x\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    So, the result is: $4 x^{2}$
  The result is: $\frac{x^{3}}{3} + 4 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 16\, dx = 16 x$
The result is: $\frac{x^{3}}{3} + 4 x^{2} + 16 x$
Now simplify:

$\frac{x \left(x^{2} + 12 x + 48\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 12 x + 48\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 12 x + 48\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                         3
 | / 2           \             2          x 
 | \x  + 8*x + 16/ dx = C + 4*x  + 16*x + --
 |                                        3 
/

$$\int \left(\left(x^{2} + 8 x\right) + 16\right)\, dx = C + \frac{x^{3}}{3} + 4 x^{2} + 16 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-42

$$-42$$

-42

$$-42$$

-42

Numerical answer [src]

-42.0

-42.0

The graph

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

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Identical expressions

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Integral of x^2+8x+16 dx

Limits of integration:

The graph:

Piecewise:

The solution