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Graphing y =:
sqrt(x^2+6)
Identical expressions
sqrt(x^ two + six)
square root of (x squared plus 6)
square root of (x to the power of two plus six)
√(x^2+6)
sqrt(x2+6)
sqrtx2+6
sqrt(x²+6)
sqrt(x to the power of 2+6)
sqrtx^2+6
sqrt(x^2+6)dx
Similar expressions
sqrt(x^2-6)

Integral of sqrt(x^2+6) dx

The solution

You have entered [src]

 11               
  /               
 |                
 |            2   
 |    / 2    \    
 |  t*\x  + 6/  dx
 |                
/                 
1

$$\int\limits_{1}^{11} t \left(x^{2} + 6\right)^{2}\, dx$$

Integral(t*(x^2 + 6)^2, (x, 1, 11))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int t \left(x^{2} + 6\right)^{2}\, dx = t \int \left(x^{2} + 6\right)^{2}\, dx$
1. Rewrite the integrand:
  
  $\left(x^{2} + 6\right)^{2} = x^{4} + 12 x^{2} + 36$
2. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{4}\, dx = \frac{x^{5}}{5}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 12 x^{2}\, dx = 12 \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $4 x^{3}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 36\, dx = 36 x$
  The result is: $\frac{x^{5}}{5} + 4 x^{3} + 36 x$
So, the result is: $t \left(\frac{x^{5}}{5} + 4 x^{3} + 36 x\right)$
Now simplify:

$\frac{t x \left(x^{4} + 20 x^{2} + 180\right)}{5}$
Add the constant of integration:

$\frac{t x \left(x^{4} + 20 x^{2} + 180\right)}{5}+ \mathrm{constant}$

The answer is:

$\frac{t x \left(x^{4} + 20 x^{2} + 180\right)}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                          
 |           2            /               5\
 |   / 2    \             |   3          x |
 | t*\x  + 6/  dx = C + t*|4*x  + 36*x + --|
 |                        \              5 /
/

$$\int t \left(x^{2} + 6\right)^{2}\, dx = C + t \left(\frac{x^{5}}{5} + 4 x^{3} + 36 x\right)$$

Simplify

The answer [src]

37890*t

$$37890 t$$

37890*t

$$37890 t$$

37890*t

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

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Integral of sqrt(x^2+6) dx

Limits of integration:

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Piecewise:

The solution