What is the integral of 5^{2-3x} ?

The integral of 5^{2-3x} is -(5^{2-3x})/(3ln(5))+C

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integral of 5^{2-3x}

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

- \frac{5 ^{2 - 3 x}}{3 ln ( 5 )} + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{3} \cdot 5^{u} d u

= \int - \frac{1}{3} \cdot 5^{u} d u

Take the constant out:

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

= - \frac{1}{3} \cdot \int 5^{u} d u

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

= - \frac{1}{3} \cdot \frac{5 ^{u}}{ln ( 5 )}

Substitute back

u = 2 - 3 x

= - \frac{1}{3} \cdot \frac{5 ^{2 - 3 x}}{ln ( 5 )}

Simplify

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

= - \frac{5 ^{2 - 3 x}}{3 ln ( 5 )}

Add a constant to the solution

= - \frac{5 ^{2 - 3 x}}{3 ln ( 5 )} + C

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What is the integral of 5^{2-3x} ?
The integral of 5^{2-3x} is -(5^{2-3x})/(3ln(5))+C