I don't know how to solve this indefinite integral with both limits as variables:
^x^3
�ç (z^4+1)dz
⌄ln(x)
If you could explain I'd appreciate it.
just do it as usual.
∫[lnx,x^3] (z^4+1) dz
= 1/5 z^5 + z [lnx,x^3]
= (1/5 x^15 + x^3)-(1/5 ln^5(x) + ln(x))
Not very pretty, but c'est la vie...
thank you steve
To solve the indefinite integral ∫(x^3 / (ln(x)) × (z^4+1) dz), where both the limits are variables, we need to follow the steps below:
Step 1: Identify the function to integrate.
In this case, the function is (x^3 / (ln(x)) × (z^4+1).
Step 2: Use the properties of indefinite integrals.
Since both limits, ^x and ⌄ln(x), are variables, we need to integrate the function with respect to z while treating x and ln(x) as constants.
Step 3: Integrate the function.
To integrate the function (x^3 / (ln(x)) × (z^4+1)) with respect to z, we can treat x and ln(x) as constants. The integral of (z^4+1) dz is (z^5/5 + z).
Step 4: Apply the result from Step 3.
The indefinite integral of the given function becomes:
∫((x^3 / (ln(x)) × (z^4+1)) dz = (x^3 / (ln(x)) × (z^5/5 + z)) + C,
where C is the constant of integration.
So, the solution to the indefinite integral with both limits as variables is (x^3 / (ln(x)) × (z^5/5 + z)) + C.