Mister Exam

Other calculators

x^4+2x^2+1
Solving integrals/ x^4+2x^2+1

Integral of x^4+2x^2+1 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |  / 4      2    \   
 |  \x  + 2*x  + 1/ dx
 |                    
/                     
-1
∫−11((x4+2x2)+1) dx\int\limits_{-1}^{1} \left(\left(x^{4} + 2 x^{2}\right) + 1\right)\, dx 
Integral(x^4 + 2*x^2 + 1, (x, -1, 1))
Detail solution

  1. Integrate term-by-term:

    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:

        ∫2x2 dx=2∫x2 dx\int 2 x^{2}\, dx = 2 \int x^{2}\, dx

        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}

        So, the result is: 2x33\frac{2 x^{3}}{3}

      The result is: x55+2x33\frac{x^{5}}{5} + \frac{2 x^{3}}{3}

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

      ∫1 dx=x\int 1\, dx = x

    The result is: x55+2x33+x\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + x

  2. Add the constant of integration:

    x55+2x33+x+constant\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + x+ \mathrm{constant}

The answer is:

x55+2x33+x+constant\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + x+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                      
 |                               5      3
 | / 4      2    \              x    2*x 
 | \x  + 2*x  + 1/ dx = C + x + -- + ----
 |                              5     3  
/
∫((x4+2x2)+1) dx=C+x55+2x33+x\int \left(\left(x^{4} + 2 x^{2}\right) + 1\right)\, dx = C + \frac{x^{5}}{5} + \frac{2 x^{3}}{3} + x
Simplify
The graph
-1.0-0.8-0.6-0.4-0.21.00.00.20.40.60.85-5
Plot the graph f(x)
The answer [src] 
56
--
15
5615\frac{56}{15} 
=
= 
56
--
15
5615\frac{56}{15} 
56/15
Numerical answer [src] 
3.73333333333333
3.73333333333333
The graph
Integral of x^4+2x^2+1 dx

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

    © Mister Exam – Calculator