# What is #int_0^pi (lnx)^2 / x^(1/2)#?

First Integration by Parts

Thus

Second Integration by Parts

Thus

Putting it together, we get

Now we can evaluate the original definite integral.

By signing up, you agree to our Terms of Service and Privacy Policy

The integral ∫₀ᴾᴵ (ln(x))² / √(x) dx evaluates to π²/2.

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.

- What is the antiderivative of #(5/x)^2#?
- How do you integrate #int (3-x)7^((3-x) ^2)dx#?
- How do you use the summation formulas to rewrite the expression #Sigma (4i^2(i-1))/n^4# as k=1 to n without the summation notation and then use the result to find the sum for n=10, 100, 1000, and 10000?
- How do you evaluate the integral #int sqrt(x^2-1)dx#?
- How do you evaluate the definite integral #int dx / ( x(sqrt(ln(x)))# from #[e, e^81]#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7