integral de 2 a 5 de 4/(9+(x-2)^2)

Solución

\int_{2}^{5} \frac{4}{9 + ( x - 2 ) ^{2}} d x

\frac{π}{3}

Notación decimal

1.04719 \dots

Pasos de solución

\int_{2}^{5} \frac{4}{9 + ( x - 2 ) ^{2}} d x

Sacar la constante:

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

= 4 \cdot \int_{2}^{5} \frac{1}{9 + ( x - 2 ) ^{2}} d x

Aplicar integración por sustitución

: \int_{0}^{3} \frac{1}{9 + u ^{2}} d u

= 4 \cdot \int_{0}^{3} \frac{1}{9 + u ^{2}} d u

Aplicar integración por sustitución

= 4 \cdot \int_{0}^{1} \frac{1}{3 ( v ^{2} + 1 )} d v

Sacar la constante:

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

= 4 \cdot \frac{1}{3} \cdot \int_{0}^{1} \frac{1}{v ^{2} + 1} d v

Aplicar la regla de integración:

\int \frac{1}{v ^{2} + 1} d v = arctan (v)

= 4 \cdot \frac{1}{3} [arctan (v)]_{0}^{1}

Simplificar

4 \cdot \frac{1}{3} [arctan (v)]_{0}^{1} : \frac{4}{3} [arctan (v)]_{0}^{1}

= \frac{4}{3} [arctan (v)]_{0}^{1}

Calcular los limites:

\frac{π}{4}

= \frac{4}{3} \cdot \frac{π}{4}

Simplificar

= \frac{π}{3}

f (x) = ln (169 sin^{2} (x))

\int e^{t a n (8 x)} sec^{2} (8 x) d x

\frac{d}{d x} (8 x + 6 x^{\frac{3}{4}})

\int \frac{4}{1 + x} d x

\int (2 x - 1) ln (x) d x