What is the integral of ((9^9)^9)^x ?

The integral of ((9^9)^9)^x is (3^{162x-4})/(2ln(3))+C

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integral of ((9^9)^9)^x

integral

((9^{9})^{9})^{x}

\frac{3 ^{162 x - 4}}{2 ln ( 3 )} + C

Solution steps

\int ((9^{9})^{9})^{x} d x

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

= \frac{( ( 9 ^{9} ) ^{9} ) ^{x}}{ln ( ( 9 ^{9} ) ^{9} )}

Simplify

\frac{( ( 9 ^{9} ) ^{9} ) ^{x}}{ln ( ( 9 ^{9} ) ^{9} )} : \frac{3 ^{162 x - 4}}{2 ln ( 3 )}

= \frac{3 ^{162 x - 4}}{2 ln ( 3 )}

Add a constant to the solution

= \frac{3 ^{162 x - 4}}{2 ln ( 3 )} + C

(sin^{2} (x))^{2}

x^{2} \cdot e^{- x}

\frac{1}{( 1 + sin ^{2} ( x ) )}

x - 2 sin (x)

\frac{x - 1}{( x + 1 ) ^{3}}

What is the integral of ((9^9)^9)^x ?
The integral of ((9^9)^9)^x is (3^{162x-4})/(2ln(3))+C