Mister Exam

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Derivative of:
ax^2+bx
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ax^ two +bx
ax squared plus bx
ax to the power of two plus bx
ax2+bx
ax²+bx
ax to the power of 2+bx
ax^2+bxdx
Similar expressions
ax^2-bx

Integral of ax^2+bx dx

The solution

You have entered [src]

  b                
  /                
 |                 
 |  /   2      \   
 |  \a*x  + b*x/ dx
 |                 
/                  
0

$$\int\limits_{0}^{b} \left(a x^{2} + b x\right)\, dx$$

Integral(a*x^2 + b*x, (x, 0, b))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int a x^{2}\, dx = a \int x^{2}\, dx$
  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: $\frac{a x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int b x\, dx = b \int x\, dx$
  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: $\frac{b x^{2}}{2}$
The result is: $\frac{a x^{3}}{3} + \frac{b x^{2}}{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                 
 |                          2      3
 | /   2      \          b*x    a*x 
 | \a*x  + b*x/ dx = C + ---- + ----
 |                        2      3  
/

$$\int \left(a x^{2} + b x\right)\, dx = C + \frac{a x^{3}}{3} + \frac{b x^{2}}{2}$$

Simplify

The answer [src]

 3      3
b    a*b 
-- + ----
2     3

$$\frac{a b^{3}}{3} + \frac{b^{3}}{2}$$

 3      3
b    a*b 
-- + ----
2     3

$$\frac{a b^{3}}{3} + \frac{b^{3}}{2}$$

Упростить

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

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Integral of ax^2+bx dx

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The solution