integral de (4^{cot(5x)})/(sin^2(5x))

Solución

\int \frac{4 ^{c o t (5 x)}}{sin ^{2} ( 5 x )} d x

- \frac{2 ^{2 c o t (5 x) - 1}}{5 ln ( 2 )} + C

Pasos de solución

\int \frac{4 ^{c o t (5 x)}}{sin ^{2} ( 5 x )} d x

Aplicar integración por sustitución

: \int \frac{4 ^{c o t (u)}}{5 sin ^{2} ( u )} d u

= \int \frac{4 ^{c o t (u)}}{5 sin ^{2} ( u )} d u

Sacar la constante:

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

= \frac{1}{5} \cdot \int \frac{4 ^{c o t (u)}}{sin ^{2} ( u )} d u

Utilizar la identidad trigonométrica básica:

\frac{1}{sin ( x )} = csc (x)

= \frac{1}{5} \cdot \int 4^{c o t (u)} csc^{2} (u) d u

Aplicar integración por sustitución

: \int - 4^{v} d v

= \frac{1}{5} \cdot \int - 4^{v} d v

Sacar la constante:

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

= \frac{1}{5} (- \int 4^{v} d v)

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

= \frac{1}{5} (- \frac{4 ^{v}}{ln ( 4 )})

Sustitución hacia atrás

= \frac{1}{5} (- \frac{4 ^{c o t (5 x)}}{ln ( 4 )})

Simplificar

\frac{1}{5} (- \frac{4 ^{c o t (5 x)}}{ln ( 4 )}) : - \frac{2 ^{2 c o t (5 x) - 1}}{5 ln ( 2 )}

= - \frac{2 ^{2 c o t (5 x) - 1}}{5 ln ( 2 )}

Agregar una constante a la solución

= - \frac{2 ^{2 c o t (5 x) - 1}}{5 ln ( 2 )} + C

\int \frac{1}{2 ( x + \frac{5}{4} ) ^{2} - \frac{33}{8}} d x

\int x^{2} - 9 x d x

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

f (x) = (x - 6) (x + 9) (x - 8)

\int \frac{x - 9}{( x + 5 ) \cdot ( x - 2 )} d x