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

Integral of x-x^3 dx

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∫−11(−x3+x) dx\int\limits_{-1}^{1} \left(- x^{3} + x\right)\, dx 
Integral(x - x^3, (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:

      ∫(−x3) dx=−∫x3 dx\int \left(- x^{3}\right)\, dx = - \int x^{3}\, dx

      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}

      So, the result is: −x44- \frac{x^{4}}{4}

    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}

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

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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∫(−x3+x) dx=C−x44+x22\int \left(- x^{3} + x\right)\, dx = C - \frac{x^{4}}{4} + \frac{x^{2}}{2}
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Integral of x-x^3 dx

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

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