What is the integral of 100(0.6)^x ?

The integral of 100(0.6)^x is -195.76151…*0.6^x+C

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integral of 100(0.6)^x

\int 100 (0.6)^{x} d x

- 195.76151 \dots \cdot 0. 6^{x} + C

Solution steps

\int 100 \cdot 0. 6^{x} d x

Take the constant out:

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

= 100 \cdot \int 0. 6^{x} d x

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

= 100 \cdot \frac{0. 6 ^{x}}{ln ( 0.6 )}

Simplify

100 \cdot \frac{0. 6 ^{x}}{ln ( 0.6 )} : - 195.76151 \dots \cdot 0. 6^{x}

= - 195.76151 \dots \cdot 0. 6^{x}

Add a constant to the solution

= - 195.76151 \dots \cdot 0. 6^{x} + C

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What is the integral of 100(0.6)^x ?
The integral of 100(0.6)^x is -195.76151…*0.6^x+C