What is the integral of (2^x3^x5^x)/2 ?

The integral of (2^x3^x5^x)/2 is (15^x*2^{x-1})/(ln(30))+C

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integral of (2^x3^x5^x)/2

\int \frac{2 ^{x} 3 ^{x} 5 ^{x}}{2} d x

\frac{1 5 ^{x} \cdot 2 ^{x - 1}}{ln ( 30 )} + C

Solution steps

\int \frac{2 ^{x} \cdot 3 ^{x} \cdot 5 ^{x}}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int 2^{x} \cdot 3^{x} \cdot 5^{x} d x

Simplify

2^{x} \cdot 3^{x} \cdot 5^{x} : 3 0^{x}

= \frac{1}{2} \cdot \int 3 0^{x} d x

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

= \frac{1}{2} \cdot \frac{3 0 ^{x}}{ln ( 30 )}

Simplify

\frac{1}{2} \cdot \frac{3 0 ^{x}}{ln ( 30 )} : \frac{1 5 ^{x} \cdot 2 ^{x - 1}}{ln ( 30 )}

= \frac{1 5 ^{x} \cdot 2 ^{x - 1}}{ln ( 30 )}

Add a constant to the solution

= \frac{1 5 ^{x} \cdot 2 ^{x - 1}}{ln ( 30 )} + C

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What is the integral of (2^x3^x5^x)/2 ?
The integral of (2^x3^x5^x)/2 is (15^x*2^{x-1})/(ln(30))+C