What is the integral of 5^{2x-7} ?

The integral of 5^{2x-7} is (5^{2x-7})/(2ln(5))+C

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integral of 5^{2x-7}

integral

5^{2 x - 7}

\frac{5 ^{2 x - 7}}{2 ln ( 5 )} + C

Solution steps

\int 5^{2 x - 7} d x

Apply u-substitution

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

= \int 5^{u} \cdot \frac{1}{2} 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 = 2 x - 7

= \frac{1}{2} \cdot \frac{5 ^{2 x - 7}}{ln ( 5 )}

Simplify

\frac{1}{2} \cdot \frac{5 ^{2 x - 7}}{ln ( 5 )} : \frac{5 ^{2 x - 7}}{2 ln ( 5 )}

= \frac{5 ^{2 x - 7}}{2 ln ( 5 )}

Add a constant to the solution

= \frac{5 ^{2 x - 7}}{2 ln ( 5 )} + C

y = x^{3} (e^{x})^{4}

\frac{1}{3 x ^{2} - 3 x}

8 y^{3}

cos (y^{3})

\frac{( e ^{t} ) ^{2}}{( e ^{2 t} + 1 )}

What is the integral of 5^{2x-7} ?
The integral of 5^{2x-7} is (5^{2x-7})/(2ln(5))+C