integral from 1 to 3 of 1/(sqrt(x^2-1))

الحلّ

\int_{1}^{3} \frac{1}{x ^{2} - 1} d x

ln (22 + 3)

العشري

1.76274 \dots

خطوات الحلّ

\int_{1}^{3} \frac{1}{x ^{2} - 1} d x

Apply Trigonometric Substitution

: \int_{0}^{arcsec (3)} sec (u) d u

= \int_{0}^{arcsec (3)} sec (u) d u

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

:استخدم التكامل البسيط

= [ln ∣ tan (u) + sec (u) ∣]_{0}^{arcsec (3)}

احسب التكامل المحدّد:

ln (22 + 3)

= ln (22 + 3)

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