What is the integral of 1000*2^x ?

The integral of 1000*2^x is (125*2^{x+3})/(ln(2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1000*2^x

\int 1000 \cdot 2^{x} d x

\frac{125 \cdot 2 ^{x + 3}}{ln ( 2 )} + C

Solution steps

\int 1000 \cdot 2^{x} d x

Take the constant out:

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

= 1000 \cdot \int 2^{x} d x

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

= 1000 \cdot \frac{2 ^{x}}{ln ( 2 )}

Simplify

1000 \cdot \frac{2 ^{x}}{ln ( 2 )} : \frac{125 \cdot 2 ^{x + 3}}{ln ( 2 )}

= \frac{125 \cdot 2 ^{x + 3}}{ln ( 2 )}

Add a constant to the solution

= \frac{125 \cdot 2 ^{x + 3}}{ln ( 2 )} + C

\int \frac{sec ^{2} ( ln ( z ) )}{z} d z

\int 2 cos (\frac{π}{3} x) d x

\int \frac{1}{2 u ^{2}} d u

\int cos (2 z) d z

\int \frac{1}{x ( x ^{5} + 1 ) ^{2}} d x

What is the integral of 1000*2^x ?
The integral of 1000*2^x is (125*2^{x+3})/(ln(2))+C