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Identical expressions
exp(x^ two +6x+ one)*(x+ three)
exponent of (x squared plus 6x plus 1) multiply by (x plus 3)
exponent of (x to the power of two plus 6x plus one) multiply by (x plus three)
exp(x2+6x+1)*(x+3)
expx2+6x+1*x+3
exp(x²+6x+1)*(x+3)
exp(x to the power of 2+6x+1)*(x+3)
exp(x^2+6x+1)(x+3)
exp(x2+6x+1)(x+3)
expx2+6x+1x+3
expx^2+6x+1x+3
exp(x^2+6x+1)*(x+3)dx
Similar expressions
exp(x^2+6x+1)*(x-3)
exp(x^2-6x+1)*(x+3)
exp(x^2+6x-1)*(x+3)

Solving integrals/ exp(x^2+6x+1)*(x+3)

Integral of exp(x^2+6x+1)*(x+3) dx

The solution

You have entered [src]

  1                         
  /                         
 |                          
 |    2                     
 |   x  + 6*x + 1           
 |  e            *(x + 3) dx
 |                          
/                           
0

$$\int\limits_{0}^{1} \left(x + 3\right) e^{x^{2} + 6 x + 1}\, dx$$

Simplify

Detail solution

Let $u = x^{2} + 6 x + 1$ .

Then let $du = \left(2 x + 6\right) dx$ and substitute $\frac{du}{2}$ :

$\int \frac{e^{u}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{e^{u}}{2}\, du = \frac{\int e^{u}\, du}{2}$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $\frac{e^{u}}{2}$
Now substitute $u$ back in:

$\frac{e^{x^{2} + 6 x + 1}}{2}$
Now simplify:

$\frac{e^{x^{2} + 6 x + 1}}{2}$
Add the constant of integration:

$\frac{e^{x^{2} + 6 x + 1}}{2}+ \mathrm{constant}$

The answer is:

$\frac{e^{x^{2} + 6 x + 1}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                            
 |                                  2          
 |   2                             x  + 6*x + 1
 |  x  + 6*x + 1                  e            
 | e            *(x + 3) dx = C + -------------
 |                                      2      
/

$${{e^{x^2+6\,x+1}}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

 8    
e    e
-- - -
2    2

$$- \frac{e}{2} + \frac{e^{8}}{2}$$

 8    
e    e
-- - -
2    2

$$- \frac{e}{2} + \frac{e^{8}}{2}$$

Simplify

Numerical answer [src]

1489.11985260663

1489.11985260663

The graph

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

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Identical expressions

Similar expressions

Integral of exp(x^2+6x+1)*(x+3) dx

Limits of integration:

The graph:

Piecewise:

The solution