You entered:
What you mean?
Integral of x^2/2x^3+1dx dx
The solution
Detail solution
-
Integrate term-by-term:
-
The integral of a constant times a function is the constant times the integral of the function:
∫2x2x3dx=2∫x2x3dx
-
There are multiple ways to do this integral.
Method #1
-
Let u=x2.
Then let du=2xdx and substitute 2du:
∫4u2du
-
The integral of a constant times a function is the constant times the integral of the function:
∫2u2du=2∫u2du
-
The integral of un is n+1un+1 when n=−1:
∫u2du=3u3
So, the result is: 6u3
Now substitute u back in:
Method #2
-
Let u=x3.
Then let du=3x2dx and substitute 3du:
∫9udu
-
The integral of a constant times a function is the constant times the integral of the function:
∫3udu=3∫udu
-
The integral of un is n+1un+1 when n=−1:
∫udu=2u2
So, the result is: 6u2
Now substitute u back in:
So, the result is: 12x6
-
The integral of a constant is the constant times the variable of integration:
∫1⋅1dx=x
The result is: 12x6+x
-
Add the constant of integration:
12x6+x+constant
The answer is:
12x6+x+constant
The answer (Indefinite)
[src]
/
|
| / 2 3 \ 6
| |x *x | x
| |----- + 1*1| dx = C + x + --
| \ 2 / 12
|
/
12x6+x
The graph
Use the examples entering the upper and lower limits of integration.