en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5/3)^x

Solution

\int (\frac{5}{3})^{x} d x

Solution

\frac{5 ^{x}}{ln ( \frac{5}{3} ) \cdot 3 ^{x}} + C

Solution steps

\int (\frac{5}{3})^{x} d x

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

= \frac{( \frac{5}{3} ) ^{x}}{ln ( \frac{5}{3} )}

Simplify

\frac{( \frac{5}{3} ) ^{x}}{ln ( \frac{5}{3} )} : \frac{5 ^{x}}{ln ( \frac{5}{3} ) \cdot 3 ^{x}}

= \frac{5 ^{x}}{ln ( \frac{5}{3} ) \cdot 3 ^{x}}

Add a constant to the solution

= \frac{5 ^{x}}{ln ( \frac{5}{3} ) \cdot 3 ^{x}} + C

Popular Examples

derivative of e^{-x}+1

\frac{d}{d x} (e^{- x} + 1)

d/(dt)(1/(sqrt(t)))

\frac{d}{d t} (\frac{1}{t})

integral of sec(x)(sec(x)-tan(x))

\int sec (x) (sec (x) - tan (x)) d x

integral from 0 to 1 of sqrt(1+(x)^2)

\int_{0}^{1} 1 + (x)^{2} d x

tangent of (x-3)(x^2+6)tangent of

(x - 3) (x^{2} + 6)

Frequently Asked Questions (FAQ)

What is the integral of (5/3)^x ?
The integral of (5/3)^x is (5^x)/(ln(5/3)*3^x)+C