Popular >

integral de (sqrt(x^2-4))/(3x^3)

Solución

\int \frac{x ^{2} - 4}{3 x ^{3}} d x

\frac{1}{3} (- \frac{x ^{2} - 4}{2 x ^{2}} + \frac{1}{4} arcsec (\frac{1}{2} x)) + C

Pasos de solución

\int \frac{x ^{2} - 4}{3 x ^{3}} d x

Sacar la constante:

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

= \frac{1}{3} \cdot \int \frac{x ^{2} - 4}{x ^{3}} d x

Aplicar integración por partes

: - \frac{x ^{2} - 4}{2 x ^{2}} - \int - \frac{1}{2 x x ^{2} - 4} d x

= \frac{1}{3} (- \frac{x ^{2} - 4}{2 x ^{2}} - \int - \frac{1}{2 x x ^{2} - 4} d x)

\int - \frac{1}{2 x x ^{2} - 4} d x = - \frac{1}{4} arcsec (\frac{1}{2} x)

= \frac{1}{3} (- \frac{x ^{2} - 4}{2 x ^{2}} - (- \frac{1}{4} arcsec (\frac{1}{2} x)))

Simplificar

= \frac{1}{3} (- \frac{x ^{2} - 4}{2 x ^{2}} + \frac{1}{4} arcsec (\frac{1}{2} x))

Agregar una constante a la solución

= \frac{1}{3} (- \frac{x ^{2} - 4}{2 x ^{2}} + \frac{1}{4} arcsec (\frac{1}{2} x)) + C

\int \frac{x ^{2} - 5 x + 3}{( x - 1 ) ( x - 2 ) ^{2}} d x

\int \frac{ln ( x )}{x ( 4 + ln ^{2} ( x ) )} d x

\int \frac{e ^{x} ( x ^{2} + 1 )}{( x + 1 ) ^{2}} d x

\int x (2^{x}) d x

\int 30 sin (4 x - 2) cos (x + 1) d x