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Integral of d{x}:
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Integral of 7x^3+4x^2
Identical expressions
7x^ three +4x^ two
7x cubed plus 4x squared
7x to the power of three plus 4x to the power of two
7x3+4x2
7x³+4x²
7x to the power of 3+4x to the power of 2
7x^3+4x^2dx
Similar expressions
7x^3-4x^2

Solving integrals/ 7x^3+4x^2

Integral of 7x^3+4x^2 dx

The solution

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  1                 
  /                 
 |                  
 |  /   3      2\   
 |  \7*x  + 4*x / dx
 |                  
/                   
0

$$\int\limits_{0}^{1} \left(7 x^{3} + 4 x^{2}\right)\, dx$$

Integral(7*x^3 + 4*x^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 7 x^{3}\, dx = 7 \int x^{3}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  So, the result is: $\frac{7 x^{4}}{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4 x^{2}\, dx = 4 \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $\frac{4 x^{3}}{3}$
The result is: $\frac{7 x^{4}}{4} + \frac{4 x^{3}}{3}$
Now simplify:

$\frac{x^{3} \cdot \left(21 x + 16\right)}{12}$
Add the constant of integration:

$\frac{x^{3} \cdot \left(21 x + 16\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \cdot \left(21 x + 16\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                           3      4
 | /   3      2\          4*x    7*x 
 | \7*x  + 4*x / dx = C + ---- + ----
 |                         3      4  
/

$${{7\,x^4}\over{4}}+{{4\,x^3}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

37
--
12

$${{37}\over{12}}$$

37
--
12

$$\frac{37}{12}$$

Simplify

Numerical answer [src]

3.08333333333333

3.08333333333333

The graph

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

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Integral of 7x^3+4x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution