How do you integrate #int (2-sqrtx)^5/sqrtx# using substitution?
Substitute:
thus:
and undoing the substitution:
By signing up, you agree to our Terms of Service and Privacy Policy
To integrate (\int (2-\sqrt{x})^5/\sqrt{x}) using substitution, let (u = 2 - \sqrt{x}). Then, (x = (2 - u)^2 = 4 - 4u + u^2), and (du = -\frac{1}{2\sqrt{x}} dx). Substituting these into the integral, we get: (\int (2 - \sqrt{x})^5/\sqrt{x} dx = -2 \int u^5 du). Integrate (u^5) to get (-\frac{1}{6}u^6 + C). Substitute (u = 2 - \sqrt{x}) back in to get the final answer: (-\frac{1}{6}(2 - \sqrt{x})^6 + C).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you use integration by parts to evaluate the integral #2xsin(x)dx#?
- How do you evaluate the integral #int sqrt(1-1/x^2)#?
- What is #f(x) = int xsinx^2 + tan^2x -cosx dx# if #f(0)=-1 #?
- How do you integrate #int xcos(5x)# by integration by parts method?
- How do you integrate #int re^(r/2)# by integration by parts method?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7