integral de (sec^3(x))/(tan(x))

Solución

\int \frac{sec ^{3} ( x )}{tan ( x )} d x

sec (x) + ln tan (\frac{x}{2}) + C

Pasos de solución

\int \frac{sec ^{3} ( x )}{tan ( x )} d x

Re-escribir usando identidades trigonométricas

= \int \frac{sec ^{3} ( x ) cos ( x )}{sin ( x )} d x

Utilizar la identidad trigonométrica básica:

\frac{cos ( x )}{sin ( x )} = cot (x)

= \int sec^{3} (x) cot (x) d x

Re-escribir usando identidades trigonométricas

= \int \frac{sec ^{2} ( x )}{sin ( x )} d x

Aplicar integración por partes

: sec (x) - \int - cot (x) csc (x) tan (x) d x

= sec (x) - \int - cot (x) csc (x) tan (x) d x

\int - cot (x) csc (x) tan (x) d x = - ln tan (\frac{x}{2})

= sec (x) - (- ln tan (\frac{x}{2}))

Simplificar

= sec (x) + ln tan (\frac{x}{2})

Agregar una constante a la solución

= sec (x) + ln tan (\frac{x}{2}) + C

x \to e lim (ln ∣ 3 x ∣)

25 y^{^{''}} - y = x e^{\frac{x}{5}}

1 e^{x}

y d x + (y cos (\frac{x}{y}) - x) d y = 0

x \to 4 lim (3 x + 2)