en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(2)2^x

Solution

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

Solution

2^{x} + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

\int a^{x} d x = \frac{a ^{x}}{ln a}

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

Simplify

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

= 2^{x}

Add a constant to the solution

= 2^{x} + C

Popular Examples

integral of x^5-3x+8

\int x^{5} - 3 x + 8 d x

integral of 1/100 x

\int \frac{1}{100} x d x

integral of (2tan(x))/(cos(2x))

\int \frac{2 tan ( x )}{cos ( 2 x )} d x

integral of (4x^3)/(sqrt(1-x^8))

\int \frac{4 x ^{3}}{1 - x ^{8}} d x

integral of x^5+7sqrt(x)

\int x^{5} + 7 x d x

Frequently Asked Questions (FAQ)

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