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(x^2-9x^4)
Solving integrals/ (x^2-9x^4)

Integral of (x^2-9x^4) dx

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The solution

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  1               
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 |  / 2      4\   
 |  \x  - 9*x / dx
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-1
∫−11(−9x4+x2) dx\int\limits_{-1}^{1} \left(- 9 x^{4} + x^{2}\right)\, dx 
Integral(x^2 - 9*x^4, (x, -1, 1))
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:

      ∫(−9x4) dx=−∫9x4 dx\int \left(- 9 x^{4}\right)\, dx = - \int 9 x^{4}\, dx

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

        ∫9x4 dx=9∫x4 dx\int 9 x^{4}\, dx = 9 \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: 9x55\frac{9 x^{5}}{5}

      So, the result is: −9x55- \frac{9 x^{5}}{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: −9x55+x33- \frac{9 x^{5}}{5} + \frac{x^{3}}{3}

  2. Now simplify:

    x3⋅(5−27x2)15\frac{x^{3} \cdot \left(5 - 27 x^{2}\right)}{15}

  3. Add the constant of integration:

    x3⋅(5−27x2)15+constant\frac{x^{3} \cdot \left(5 - 27 x^{2}\right)}{15}+ \mathrm{constant}

The answer is:

x3⋅(5−27x2)15+constant\frac{x^{3} \cdot \left(5 - 27 x^{2}\right)}{15}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                              
 |                         5    3
 | / 2      4\          9*x    x 
 | \x  - 9*x / dx = C - ---- + --
 |                       5     3 
/
x33−9 x55{{x^3}\over{3}}-{{9\,x^5}\over{5}}
Simplify
The graph
-1.0-0.8-0.6-0.4-0.21.00.00.20.40.60.8-1010
Plot the graph f(x)
The answer [src] 
-44 
----
 15
−4415-{{44}\over{15}} 
=
= 
-44 
----
 15
−4415- \frac{44}{15}
Simplify
Numerical answer [src] 
-2.93333333333333
-2.93333333333333
The graph
Integral of (x^2-9x^4) dx

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

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