en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(4)4^x

Solution

\int ln (4) 4^{x} d x

Solution

4^{x} + C

Solution steps

\int ln (4) \cdot 4^{x} d x

Take the constant out:

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

= ln (4) \cdot \int 4^{x} d x

ln (4) = 2 ln (2)

= 2 ln (2) \cdot \int 4^{x} d x

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

= 2 ln (2) \frac{4 ^{x}}{ln ( 4 )}

Simplify

2 ln (2) \frac{4 ^{x}}{ln ( 4 )} : 4^{x}

= 4^{x}

Add a constant to the solution

= 4^{x} + C

Popular Examples

integral of xsqrt((x^2+4))

\int x (x^{2} + 4) d x

integral of (4x^3-8x^2+3)/(x^2-2x)

\int \frac{4 x ^{3} - 8 x ^{2} + 3}{x ^{2} - 2 x} d x

integral of (5x^2)/((16+x^2)^2)

\int \frac{5 x ^{2}}{( 16 + x ^{2} ) ^{2}} d x

integral of 11xsin(x)cos(x)

\int 11 x sin (x) cos (x) d x

integral of 1/(t^2)sin(3/t+6)

\int \frac{1}{t ^{2}} sin (\frac{3}{t} + 6) d t

Frequently Asked Questions (FAQ)

What is the integral of ln(4)4^x ?
The integral of ln(4)4^x is 4^x+C