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Solving integrals/ (x²-5x⁴)dx

Integral of (x²-5x⁴)dx dx

Limits of integration:

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The graph:

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The solution

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  4               
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 |  \x  - 5*x / dx
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2
∫24(−5x4+x2) dx\int\limits_{2}^{4} \left(- 5 x^{4} + x^{2}\right)\, dx 
Integral(x^2 - 5*x^4, (x, 2, 4))
Detail solution

  1. Integrate term-by-term:

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

      ∫(−5x4) dx=−5∫x4 dx\int \left(- 5 x^{4}\right)\, dx = - 5 \int x^{4}\, dx

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

        ∫x4 dx=x55\int x^{4}\, dx = \frac{x^{5}}{5}

      So, the result is: −x5- x^{5}

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

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

    The result is: −x5+x33- x^{5} + \frac{x^{3}}{3}

  2. Add the constant of integration:

    −x5+x33+constant- x^{5} + \frac{x^{3}}{3}+ \mathrm{constant}

The answer is:

−x5+x33+constant- x^{5} + \frac{x^{3}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            
 |                            3
 | / 2      4\           5   x 
 | \x  - 5*x / dx = C - x  + --
 |                           3 
/
∫(−5x4+x2) dx=C−x5+x33\int \left(- 5 x^{4} + x^{2}\right)\, dx = C - x^{5} + \frac{x^{3}}{3}
Simplify
The graph
2.04.02.22.42.62.83.03.23.43.63.80-2000
Plot the graph f(x)
The answer [src] 
-2920/3
−29203- \frac{2920}{3} 
=
= 
-2920/3
−29203- \frac{2920}{3} 
-2920/3
Numerical answer [src] 
-973.333333333333
-973.333333333333

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

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