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Solving integrals/ x^2+c

Integral of x^2+c dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

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∫01(c+x2) dx\int\limits_{0}^{1} \left(c + x^{2}\right)\, dx 
Integral(x^2 + c, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

      ∫c dx=cx\int c\, dx = c x

    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: cx+x33c x + \frac{x^{3}}{3}

  2. Now simplify:

    x(c+x23)x \left(c + \frac{x^{2}}{3}\right)

  3. Add the constant of integration:

    x(c+x23)+constantx \left(c + \frac{x^{2}}{3}\right)+ \mathrm{constant}

The answer is:

x(c+x23)+constantx \left(c + \frac{x^{2}}{3}\right)+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(c+x2) dx=C+cx+x33\int \left(c + x^{2}\right)\, dx = C + c x + \frac{x^{3}}{3}
Simplify
The answer [src] 
1/3 + c
c+13c + \frac{1}{3} 
=
= 
1/3 + c
c+13c + \frac{1}{3} 
1/3 + c

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

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