de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 1 to 3 of 1/(4+(x-1)^2)

Lösung

\int_{1}^{3} \frac{1}{4 + ( x - 1 ) ^{2}} d x

Lösung

\frac{π}{8}

+1

Dezimale

0.39269 \dots

Schritte zur Lösung

\int_{1}^{3} \frac{1}{4 + ( x - 1 ) ^{2}} d x

Wende U-Substitution an

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

Wende integrale Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [arctan (v)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4}

= \frac{1}{2} \cdot \frac{π}{4}

Vereinfache

= \frac{π}{8}

Graph

Beliebte Beispiele

integral of 24xy^2+3ye^{xy}

\int 24 x y^{2} + 3 y e^{x y} d x

(dy)/(dx)=e^{(6x-3y)},y(0)=3

\frac{d y}{d x} = e^{(6 x - 3 y)}, y (0) = 3

integral of (2-e^x)^2

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

derivative f(x)=x^2(1-5x)

d er i v a t i v e f (x) = x^{2} (1 - 5 x)

integral of (30)/((225x^2+1)^2)

\int \frac{30}{( 225 x ^{2} + 1 ) ^{2}} d x