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

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

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integral of 5^{3-2x}

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

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

Solution steps

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

Apply u-substitution

: \int - \frac{1}{2} \cdot 5^{u} d u

= \int - \frac{1}{2} \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}{2} \cdot \int 5^{u} d u

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

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

Substitute back

u = 3 - 2 x

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

Simplify

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

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

Add a constant to the solution

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

y^{^{''}} + 2 y^{^{'}} + y = x

\frac{d}{d x} ((x + 2)^{3} - 2)

\frac{d}{d x} (tan^{3} (4 x))

\int 11 x d x

\frac{d}{d x} (arctan (x))

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