What is the integral of x^{x/(ln(x))} ?

The integral of x^{x/(ln(x))} is x^{x/(ln(x))+1}-e^xx+e^x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^{x/(ln(x))}

\int x^{\frac{x}{l n ( x )}} d x

x^{\frac{x}{l n ( x )} + 1} - e^{x} x + e^{x} + C

Solution steps

\int x^{\frac{x}{l n ( x )}} d x

Apply Integration By Parts

: x^{\frac{x}{l n ( x )} + 1} - \int e^{x} x d x

= x^{\frac{x}{l n ( x )} + 1} - \int e^{x} x d x

\int e^{x} x d x = e^{x} x - e^{x}

= x^{\frac{x}{l n ( x )} + 1} - (e^{x} x - e^{x})

Simplify

= x^{\frac{x}{l n ( x )} + 1} - e^{x} x + e^{x}

Add a constant to the solution

= x^{\frac{x}{l n ( x )} + 1} - e^{x} x + e^{x} + C

\int 2 t^{2} + 1 d t

\int \frac{2 + cot ( x )}{cos ( x )} d x

\int - 2 x cos (3 x + 4) d x

\int \frac{( x + 3 )}{x} d x

\frac{1}{x ^{\frac{3}{2}}}

What is the integral of x^{x/(ln(x))} ?
The integral of x^{x/(ln(x))} is x^{x/(ln(x))+1}-e^xx+e^x+C