What is the integral of ln(2^x) ?

The integral of ln(2^x) is 1/2 ln(2)x^2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(2^x)

\int ln (2^{x}) d x

\frac{1}{2} ln (2) x^{2} + C

Solution steps

\int ln (2^{x}) d x

Apply Integration By Parts

: ln (2) x^{2} - \int ln (2) x d x

= ln (2) x^{2} - \int ln (2) x d x

\int ln (2) x d x = \frac{1}{2} ln (2) x^{2}

= ln (2) x^{2} - \frac{1}{2} ln (2) x^{2}

Simplify

ln (2) x^{2} - \frac{1}{2} ln (2) x^{2} : \frac{1}{2} ln (2) x^{2}

= \frac{1}{2} ln (2) x^{2}

Add a constant to the solution

= \frac{1}{2} ln (2) x^{2} + C

\int 2^{x} - 4 sin (x) d x

\int \frac{x}{6 - x} d x

\frac{1}{y}

\int 4^{x} e^{2 x} d x

\int \frac{x ^{2}}{x ^{2} + 2 x - 15} d x