Evaluate $\int{ \ln(\sqrt{x})dx}$ using integration by parts

You have not done anything wrong. Simply note that $\log(\sqrt x)=\frac12 \log(x)$.

Therefore, your analysis is correct; the answer is $(B)\,\, \frac12x\log(x)-\frac12 x+C$.

Tags:

Integration

Logarithms

Related

I wake up in a random class and hear 6 biology-related words. How certain should I be that I'm in Biology class? Proving that $\sum_{n=1}^\infty \frac{\sin\left(n\frac{\pi}{3}\right)}{(2n+1)^2}=\frac{G}{\sqrt 3} -\frac{\pi^2}{24}$ Compressing the primes using simple addition? Having trouble showing a function is continuous: $x/(1+|x|)$ Derive $P \to \neg \neg P$ in a structure with not and implies How do we know our definitions don't lead to contradictions Show that $\int\limits_0^{\frac{\pi}2}4\cos^2(x)\log^2(\cos x)~\mathrm dx=-\pi\log 2+\pi\log^2 2-\frac{\pi}2+\frac{\pi^3}{12}$ How many 5 digit numbers are there, whose i digit is divisible by i? Let $a\mid bc $ then prove or disprove $a\mid (a,b)c$ Is a convex function always continuous? When does Brunn-Minkowski inequatily $(m(A+B))^{1/d} \geqslant (m(A))^{1/d} + (m(B))^{1/d}$ become equality? What does "finite but unbounded" mean?

Recent Posts