de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 9 to 16 of 1/(7-sqrt(x))

Lösung

\int_{9}^{16} \frac{1}{7 - x} d x

Lösung

2 (- 1 + 7 (2 ln (2) - ln (3)))

+1

Dezimale

2.02754 \dots

Schritte zur Lösung

\int_{9}^{16} \frac{1}{7 - x} d x

Wende U-Substitution an

= \int_{3}^{4} \frac{2 u}{7 - u} d u

Entferne die Konstante:

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

= 2 \cdot \int_{3}^{4} \frac{u}{7 - u} d u

Wende U-Substitution an

= 2 \cdot \int_{4}^{3} - \frac{- v + 7}{v} d v

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= 2 (- \int_{3}^{4} - \frac{- v + 7}{v} d v)

Entferne die Konstante:

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

= 2 (- (- \int_{3}^{4} \frac{- v + 7}{v} d v))

Multipliziere aus

\frac{- v + 7}{v} : - 1 + \frac{7}{v}

= 2 (- (- \int_{3}^{4} - 1 + \frac{7}{v} d v))

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (- (- (- \int_{3}^{4} 1 d v + \int_{3}^{4} \frac{7}{v} d v)))

\int_{3}^{4} 1 d v = 1

\int_{3}^{4} \frac{7}{v} d v = 7 (2 ln (2) - ln (3))

= 2 (- (- (- 1 + 7 (2 ln (2) - ln (3)))))

Vereinfache

= 2 (- 1 + 7 (2 ln (2) - ln (3)))

Graph

Beliebte Beispiele

integral of (sqrt(x))/(x-16)

\int \frac{x}{x - 16} d x

sum from n=0 to infinity of n^2(x)^{n-1}

n = 0 \sum \infty n^{2} (x)^{n - 1}

laplacetransform 5t^4

l a pl a ce t r an s f or m 5 t^{4}

x^7y^'=-8x^6y+cos(2x)

x^{7} y^{^{'}} = - 8 x^{6} y + cos (2 x)

integral of (-2ax)/(x^2+y^2)

\int \frac{- 2 a x}{x ^{2} + y ^{2}} d y