What is the integral of 10^{2θ} ?

The integral of 10^{2θ} is (25^θ*2^{2θ-1})/(ln(10))+C

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integral of 10^{2θ}

\int 1 0^{2 θ} d θ

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

Solution steps

\int 1 0^{2 θ} d θ

Simplify

1 0^{2 θ} : 10 0^{θ}

= \int 10 0^{θ} d θ

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

= \frac{10 0 ^{θ}}{ln ( 100 )}

Simplify

\frac{10 0 ^{θ}}{ln ( 100 )} : \frac{2 5 ^{θ} \cdot 2 ^{2 θ - 1}}{ln ( 10 )}

= \frac{2 5 ^{θ} \cdot 2 ^{2 θ - 1}}{ln ( 10 )}

Add a constant to the solution

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

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What is the integral of 10^{2θ} ?
The integral of 10^{2θ} is (25^θ*2^{2θ-1})/(ln(10))+C