integral de ((x^2+1))/(5cosh^2(x^3+3x))

Solución

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

\frac{1}{15} tanh (x^{3} + 3 x) + C

Pasos de solución

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

Sacar la constante:

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

= \frac{1}{5} \cdot \int \frac{x ^{2} + 1}{cosh ^{2} ( x ^{3} + 3 x )} d x

Aplicar integración por sustitución

: \int \frac{1}{3 cosh ^{2} ( u )} d u

= \frac{1}{5} \cdot \int \frac{1}{3 cosh ^{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 \frac{1}{3} \cdot \int \frac{1}{cosh ^{2} ( u )} d u

Utilizar la identidad hiperbólica:

\frac{1}{cosh ( x )} = sech (x)

= \frac{1}{5} \cdot \frac{1}{3} \cdot \int sech^{2} (u) d u

Aplicar la regla de integración:

\int sech^{2} (u) d u = tanh (u)

= \frac{1}{5} \cdot \frac{1}{3} tanh (u)

Sustituir en la ecuación

u = x^{3} + 3 x

= \frac{1}{5} \cdot \frac{1}{3} tanh (x^{3} + 3 x)

Simplificar

\frac{1}{5} \cdot \frac{1}{3} tanh (x^{3} + 3 x) : \frac{1}{15} tanh (x^{3} + 3 x)

= \frac{1}{15} tanh (x^{3} + 3 x)

Agregar una constante a la solución

= \frac{1}{15} tanh (x^{3} + 3 x) + C

\frac{\partial}{\partial y} (x^{2} + y^{2} - z)

\frac{\partial}{\partial y} (cos (x^{2} + y^{2}))

\int (3 x + 5) cos (\frac{x}{4}) d x

\frac{\partial}{\partial y} (3 x z + y^{2})

e^{\frac{x}{y}}