integral de sin^2(2x+5)

Solución

\int sin^{2} (2 x + 5) d x

\frac{1}{8} (2 (2 x + 5) - sin (2 (2 x + 5))) + C

Pasos de solución

\int sin^{2} (2 x + 5) d x

Re-escribir usando identidades trigonométricas

= \int \frac{1 - cos ( 2 ( 2 x + 5 ) )}{2} d x

Sacar la constante:

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

= \frac{1}{2} \cdot \int 1 - cos (2 (2 x + 5)) d x

Aplicar integración por sustitución

: \int (1 - cos (u)) \frac{1}{4} d u

= \frac{1}{2} \cdot \int (1 - cos (u)) \frac{1}{4} d u

Sacar la constante:

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

= \frac{1}{2} \cdot \frac{1}{4} \cdot \int 1 - cos (u) d u

Aplicar la regla de la suma:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} \cdot \frac{1}{4} (\int 1 d u - \int cos (u) d u)

\int 1 d u = u

\int cos (u) d u = sin (u)

= \frac{1}{2} \cdot \frac{1}{4} (u - sin (u))

Sustituir en la ecuación

u = 2 (2 x + 5)

= \frac{1}{2} \cdot \frac{1}{4} (2 (2 x + 5) - sin (2 (2 x + 5)))

Simplificar

\frac{1}{2} \cdot \frac{1}{4} (2 (2 x + 5) - sin (2 (2 x + 5))) : \frac{1}{8} (2 (2 x + 5) - sin (2 (2 x + 5)))

= \frac{1}{8} (2 (2 x + 5) - sin (2 (2 x + 5)))

Agregar una constante a la solución

= \frac{1}{8} (2 (2 x + 5) - sin (2 (2 x + 5))) + C

\frac{\partial}{\partial x} (e^{- 7 y} cos (7 x))

\frac{d y}{d x} = \frac{y}{x} + \frac{x}{2 ( y + x )}

\int_{0}^{1} (2 x + 1)^{3} d x

f (x) = 3 x + 7, (3, 4)

\frac{1}{s ( s ^{2} + 2 s + 2 )}