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Integral of d{x}:
Integral of ax^3
Integral of sin^2y
Integral of cos^2(5x)
Integral of 2tanx
Identical expressions
ax^ three
ax cubed
ax to the power of three
ax3
ax³
ax to the power of 3
ax^3dx

Solving integrals/ ax^3

Integral of ax^3 dx

The solution

You have entered [src]

$$\int\limits_{1}^{2} a x^{3}\, dx$$

Integral(a*x^3, (x, 1, 2))

Detail solution

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

$\int a x^{3}\, dx = a \int x^{3}\, dx$
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: $\frac{a x^{4}}{4}$
Add the constant of integration:

$\frac{a x^{4}}{4}+ \mathrm{constant}$

The answer is:

$\frac{a x^{4}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                  
 |                  4
 |    3          a*x 
 | a*x  dx = C + ----
 |                4  
/

$${{a\,x^4}\over{4}}$$

Simplify

The answer [src]

15*a
----
 4

$${{15\,a}\over{4}}$$

=

15*a
----
 4

$$\frac{15 a}{4}$$

Simplify

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