What is the integral of 3^{4-11x} ?

The integral of 3^{4-11x} is -(3^{4-11x})/(11ln(3))+C

integral of 3^{4-11x}

\int 3^{4 - 11 x} d x

- \frac{3 ^{4 - 11 x}}{11 ln ( 3 )} + C

Solution steps

\int 3^{4 - 11 x} d x

Apply u-substitution

= \int - \frac{1}{11} \cdot 3^{u} d u

Take the constant out:

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

= - \frac{1}{11} \cdot \int 3^{u} d u

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

= - \frac{1}{11} \cdot \frac{3 ^{u}}{ln ( 3 )}

Substitute back

u = 4 - 11 x

= - \frac{1}{11} \cdot \frac{3 ^{4 - 11 x}}{ln ( 3 )}

Simplify

- \frac{1}{11} \cdot \frac{3 ^{4 - 11 x}}{ln ( 3 )} : - \frac{3 ^{4 - 11 x}}{11 ln ( 3 )}

= - \frac{3 ^{4 - 11 x}}{11 ln ( 3 )}

Add a constant to the solution

= - \frac{3 ^{4 - 11 x}}{11 ln ( 3 )} + C

\int (x + 1) sin (x) d x

\int \frac{sin ( x )}{1 + sin ( x ) + cos ( x )} d x

\int \frac{5}{x ( ln ( x ) ) ^{4}} d x

\int \frac{1}{x ( x ^{7} + 1 )} d x

\int \frac{125}{( 5 x - 300 ) ^{2}} d x

What is the integral of 3^{4-11x} ?
The integral of 3^{4-11x} is -(3^{4-11x})/(11ln(3))+C