de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of x/((sqrt(25+x^2))^3)

Lösung

\int \frac{x}{( 25 + x ^{2} ) ^{3}} d x

Lösung

\frac{x ^{2}}{25 25 + x ^{2}} - \frac{1}{25} 25 + x^{2} + C

Schritte zur Lösung

\int \frac{x}{( 25 + x ^{2} ) ^{3}} d x

Wende Exponentenregel an:

(a^{n})^{m} = a^{n \cdot m}

(25 + x^{2})^{3} = (25 + x^{2})^{\frac{3}{2}}

= \int \frac{x}{( 25 + x ^{2} ) ^{\frac{3}{2}}} d x

25 + x^{2} = 25 (1 + \frac{x ^{2}}{25})

= \int \frac{x}{( 25 ( 1 + \frac{x ^{2}}{25} ) ) ^{\frac{3}{2}}} d x

Wende die partielle Integration an

= \frac{x ^{2}}{25 25 + x ^{2}} - \int \frac{x}{25 25 + x ^{2}} d x

\int \frac{x}{25 25 + x ^{2}} d x = \frac{1}{25} 25 + x^{2}

= \frac{x ^{2}}{25 25 + x ^{2}} - \frac{1}{25} 25 + x^{2}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{25 25 + x ^{2}} - \frac{1}{25} 25 + x^{2} + C

Graph

Beliebte Beispiele

integral of 1/(sqrt(x^2-9x))

\int \frac{1}{x ^{2} - 9 x} d x

integral of sin^7(θ)

\int sin^{7} (θ) d θ

integral of 5^{ln(x)}

\int 5^{l n (x)} d x

integral of 2x\sqrt[3]{x^2+1}

\int 2 x 3 x^{2} + 1 d x

integral of 1/(sqrt(x)(1+\sqrt{x))^4}

\int \frac{1}{x ( 1 + x ) ^{4}} d x