What is the integral from e to e^4 of 1/(xsqrt(Inx)) ?

The integral from e to e^4 of 1/(xsqrt(Inx)) is -2/(e^2sqrt(In))+2/(sqrt(eIn))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from e to e^4 of 1/(xsqrt(Inx))

\int_{e}^{e^{4}} \frac{1}{x I n x} d x

- \frac{2}{e ^{2} I n} + \frac{2}{e I n}

Solution steps

\int_{e}^{e^{4}} \frac{1}{x I n x} d x

Apply u-substitution

= \int_{I n e}^{I n e^{4}} \frac{1}{u u} d u

Simplify

u u : u^{\frac{3}{2}}

= \int_{I n e}^{I n e^{4}} \frac{1}{u ^{\frac{3}{2}}} d u

Apply the Power Rule

= [- \frac{2}{u}]_{I n e}^{I n e^{4}}

Compute the boundaries:

- \frac{2}{e ^{2} I n} + \frac{2}{e I n}

= - \frac{2}{e ^{2} I n} + \frac{2}{e I n}

What is the integral from e to e^4 of 1/(xsqrt(Inx)) ?
The integral from e to e^4 of 1/(xsqrt(Inx)) is -2/(e^2sqrt(In))+2/(sqrt(eIn))