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Solving integrals/ x^4+4x^3

Integral of x^4+4x^3 dx

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∫00(x4+4x3) dx\int\limits_{0}^{0} \left(x^{4} + 4 x^{3}\right)\, dx 
Integral(x^4 + 4*x^3, (x, 0, 0))
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:

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

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

      ∫4x3 dx=4∫x3 dx\int 4 x^{3}\, dx = 4 \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: x4x^{4}

    The result is: x55+x4\frac{x^{5}}{5} + x^{4}

  2. Now simplify:

    x4(x+5)5\frac{x^{4} \left(x + 5\right)}{5}

  3. Add the constant of integration:

    x4(x+5)5+constant\frac{x^{4} \left(x + 5\right)}{5}+ \mathrm{constant}

The answer is:

x4(x+5)5+constant\frac{x^{4} \left(x + 5\right)}{5}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \x  + 4*x / dx = C + x  + --
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∫(x4+4x3) dx=C+x55+x4\int \left(x^{4} + 4 x^{3}\right)\, dx = C + \frac{x^{5}}{5} + x^{4}
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    Use the examples entering the upper and lower limits of integration.

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