Question

integral of sqrt of x ln x dx.. ln x is outside of sqrt.

Answer 1

\[\int \sqrt{x} \ln{x}dx\]

Answer 2

Use by Parts

Answer 3

Use integration by parts: u' = sqrt(x), v = ln x, then your integral
I = (2/3)x^(3/2).ln x - (2/3) integral x^(1/2) dx

because v' = 1/x

Answer 4

\[ \frac{2}{3}\times x^{\frac{3}{2}} - \frac{2}{3}\int\frac{x^\frac{3}{2}}{x}dx \]

Answer 5

oh.. thanks master ishaan, and master JamesJ. i also used by parts but i always get back to ln x. anyways, i'll practice solve this. thanks! :D

Answer 6

(2 (x log(x))^(3/2) (3 sqrt(log(x))-sqrt(6) F(sqrt(3/2) sqrt(log(x)))))/(9 log^(3/2)(x))+constant

Answer 7

FullSimplify[((6 x^(3/2) - (Sqrt[6 Pi] Erfi[Sqrt[3/2] Sqrt[Log[x]]])/Sqrt[Log[x]]) Sqrt[x Log[x]])/(9 Sqrt[x])]

Answer 8

uh question.. i thought derivative of ln x is xlnx-x.. explain? xD

Answer 9

The derivative of ln x is 1/x.
The INTEGRAL of ln x is x ln x - x

Answer 10

The fact that \[\ln x = \int\limits_1^x \frac{dt}{t}\]
is probably the most important thing of ln x and in a careful, modern development of calculus, this is even the definition of ln x.

Answer 11

oh.. ok. thanks JamesJ! :D