What is the integral of (x^2)/((x^2-36)^{5/2)} ?

The integral of (x^2)/((x^2-36)^{5/2)} is (x^3)/(3(x^2-36)^{5/2)}-(x^5)/(108(x^2-36)^{5/2)}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x^2)/((x^2-36)^{5/2)}

\int \frac{x ^{2}}{( x ^{2} - 36 ) ^{\frac{5}{2}}} d x

\frac{x ^{3}}{3 ( x ^{2} - 36 ) ^{\frac{5}{2}}} - \frac{x ^{5}}{108 ( x ^{2} - 36 ) ^{\frac{5}{2}}} + C

Solution steps

\int \frac{x ^{2}}{( x ^{2} - 36 ) ^{\frac{5}{2}}} d x

Apply Integration By Parts

= \frac{x ^{3}}{3 ( x ^{2} - 36 ) ^{\frac{5}{2}}} - \int - \frac{5 x ^{4}}{3 ( x ^{2} - 36 ) ^{\frac{7}{2}}} d x

\int - \frac{5 x ^{4}}{3 ( x ^{2} - 36 ) ^{\frac{7}{2}}} d x = \frac{x ^{5}}{108 ( x ^{2} - 36 ) ^{\frac{5}{2}}}

= \frac{x ^{3}}{3 ( x ^{2} - 36 ) ^{\frac{5}{2}}} - \frac{x ^{5}}{108 ( x ^{2} - 36 ) ^{\frac{5}{2}}}

Add a constant to the solution

= \frac{x ^{3}}{3 ( x ^{2} - 36 ) ^{\frac{5}{2}}} - \frac{x ^{5}}{108 ( x ^{2} - 36 ) ^{\frac{5}{2}}} + C

What is the integral of (x^2)/((x^2-36)^{5/2)} ?
The integral of (x^2)/((x^2-36)^{5/2)} is (x^3)/(3(x^2-36)^{5/2)}-(x^5)/(108(x^2-36)^{5/2)}+C