What is the integral of 10^{4x+1} ?

The integral of 10^{4x+1} is (2^{4x-1}*5^{4x+1})/(ln(10))+C

integral of 10^{4x+1}

\int 1 0^{4 x + 1} d x

\frac{2 ^{4 x - 1} \cdot 5 ^{4 x + 1}}{ln ( 10 )} + C

Solution steps

\int 1 0^{4 x + 1} d x

Simplify

1 0^{4 x + 1} : 1 0^{4 x} \cdot 10

= \int 1 0^{4 x} \cdot 10 d x

Take the constant out:

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

= 10 \cdot \int 1 0^{4 x} d x

Simplify

1 0^{4 x} : 1000 0^{x}

= 10 \cdot \int 1000 0^{x} d x

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

= 10 \cdot \frac{1000 0 ^{x}}{ln ( 10000 )}

Simplify

10 \cdot \frac{1000 0 ^{x}}{ln ( 10000 )} : \frac{2 ^{4 x - 1} \cdot 5 ^{4 x + 1}}{ln ( 10 )}

= \frac{2 ^{4 x - 1} \cdot 5 ^{4 x + 1}}{ln ( 10 )}

Add a constant to the solution

= \frac{2 ^{4 x - 1} \cdot 5 ^{4 x + 1}}{ln ( 10 )} + C

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What is the integral of 10^{4x+1} ?
The integral of 10^{4x+1} is (2^{4x-1}*5^{4x+1})/(ln(10))+C