Integrate: xrootof(2+3.fourth rootof(x^3)/x^6.root(x)
plz help i do not no it at all show working!!
Do you mean
x√(2+3∜(x^3)/(x^6√x))?
I doubt it. How about some clear text with matched parentheses?
If there are higher roots, just spell them out, as
cuberoot(x), 4throot(x), etc.
Yes that's what i mean sir
I seriously doubt it. Take a look at how wolframalpha interprets that:
http://www.wolframalpha.com/input/?i=integral+x%E2%88%9A%282%2B3%E2%88%9C%28x^3%29%2F%28x^6%E2%88%9Ax%29%29
Maybe you can play around with your syntax till you get what you want.
To integrate the given expression, let's first simplify it:
xrootof(2 + 3.fourth rootof(x^3) / x^6.root(x))
= x^(1/2) * (2 + 3 * x^(3/4) / x^(6*1/2) * x^(1/2))
= x^(1/2) * (2 + 3 * x^(3/4) / x^3 * x^(1/2))
= x^(1/2) * (2 + 3 * x^(3/4) / x^(7/2))
Now, let's integrate term by term:
∫ x^(1/2) * (2 + 3 * x^(3/4) / x^(7/2)) dx
= ∫ 2x^(1/2) dx + ∫ 3 * x^(3/4) / x^(7/2) dx
= 2 * ∫ x^(1/2) dx + 3 * ∫ x^(3/4) / x^(7/2) dx
To integrate each term, use the power rule of integration.
For the first term:
∫ x^(1/2) dx = 2/3 * x^(3/2) + C
For the second term:
∫ x^(3/4) / x^(7/2) dx = 3/2 * x^(3/4 - 7/2 + 1) + C
= 3/2 * x^(-11/4) + C
Therefore, the final result is:
∫ x^(1/2) * (2 + 3 * x^(3/4) / x^(7/2)) dx = 2/3 * x^(3/2) + 3/2 * x^(-11/4) + C
where C is the constant of integration.