Mister Exam

Other calculators

x^3-5x
Solving integrals/ x^3-5x

Integral of x^3-5x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |  / 3      \   
 |  \x  - 5*x/ dx
 |               
/                
0
∫01(x3−5x) dx\int\limits_{0}^{1} \left(x^{3} - 5 x\right)\, dx 
Integral(x^3 - 5*x, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x3 dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

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

      ∫(−5x) dx=−5∫x dx\int \left(- 5 x\right)\, dx = - 5 \int x\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

      So, the result is: −5x22- \frac{5 x^{2}}{2}

    The result is: x44−5x22\frac{x^{4}}{4} - \frac{5 x^{2}}{2}

  2. Now simplify:

    x2(x2−10)4\frac{x^{2} \left(x^{2} - 10\right)}{4}

  3. Add the constant of integration:

    x2(x2−10)4+constant\frac{x^{2} \left(x^{2} - 10\right)}{4}+ \mathrm{constant}

The answer is:

x2(x2−10)4+constant\frac{x^{2} \left(x^{2} - 10\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
 |                        2    4
 | / 3      \          5*x    x 
 | \x  - 5*x/ dx = C - ---- + --
 |                      2     4 
/
∫(x3−5x) dx=C+x44−5x22\int \left(x^{3} - 5 x\right)\, dx = C + \frac{x^{4}}{4} - \frac{5 x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
-9/4
−94- \frac{9}{4} 
=
= 
-9/4
−94- \frac{9}{4} 
-9/4
Numerical answer [src] 
-2.25
-2.25
The graph
Integral of x^3-5x dx

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

    © Mister Exam – Calculator