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x^2/2x^3+1dx
Solving integrals/ x^2/2x^3+1dx

You entered:

x^2/2x^3+1dx

What you mean?

x^2*x^3/2 + 1*dx
 
x^1*x^3 + 1*dx
 
x^2/(2*x^3 + 1*dx)
 
x^2*dx/(2*x^3 + 1)
 
x^2/((2*x^3)) + 1*dx
 
x^2*3/(2*x) + 1*dx
 
x^2/((2*x)^3) + 1*dx

Integral of x^2/2x^3+1dx dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
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 |  / 2  3      \   
 |  |x *x       |   
 |  |----- + 1*1| dx
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0
∫01(x2x32+1⋅1) dx\int\limits_{0}^{1} \left(\frac{x^{2} x^{3}}{2} + 1 \cdot 1\right)\, dx 
Integral(x^2*x^3/2 + 1*1, (x, 0, 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:

      ∫x2x32 dx=∫x2x3 dx2\int \frac{x^{2} x^{3}}{2}\, dx = \frac{\int x^{2} x^{3}\, dx}{2}

      1. There are multiple ways to do this integral.

        Method #1

        1. Let u=x2u = x^{2}.

          Then let du=2xdxdu = 2 x dx and substitute du2\frac{du}{2}:

          ∫u24 du\int \frac{u^{2}}{4}\, du

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

            ∫u22 du=∫u2 du2\int \frac{u^{2}}{2}\, du = \frac{\int u^{2}\, du}{2}

            1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

              ∫u2 du=u33\int u^{2}\, du = \frac{u^{3}}{3}

            So, the result is: u36\frac{u^{3}}{6}

          Now substitute uu back in:

          x66\frac{x^{6}}{6}

        Method #2

        1. Let u=x3u = x^{3}.

          Then let du=3x2dxdu = 3 x^{2} dx and substitute du3\frac{du}{3}:

          ∫u9 du\int \frac{u}{9}\, du

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

            ∫u3 du=∫u du3\int \frac{u}{3}\, du = \frac{\int u\, du}{3}

            1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

              ∫u du=u22\int u\, du = \frac{u^{2}}{2}

            So, the result is: u26\frac{u^{2}}{6}

          Now substitute uu back in:

          x66\frac{x^{6}}{6}

      So, the result is: x612\frac{x^{6}}{12}

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

      ∫1⋅1 dx=x\int 1 \cdot 1\, dx = x

    The result is: x612+x\frac{x^{6}}{12} + x

  2. Add the constant of integration:

    x612+x+constant\frac{x^{6}}{12} + x+ \mathrm{constant}

The answer is:

x612+x+constant\frac{x^{6}}{12} + x+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
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 | / 2  3      \               6
 | |x *x       |              x 
 | |----- + 1*1| dx = C + x + --
 | \  2        /              12
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/
x612+x{{x^6}\over{12}}+x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
13
--
12
1312{{13}\over{12}} 
=
= 
13
--
12
1312\frac{13}{12}
Упростить
Numerical answer [src] 
1.08333333333333
1.08333333333333
The graph
Integral of x^2/2x^3+1dx dx

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

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