What is the integral of (t^2)/((t^2-9)^{5/2)} ?

The integral of (t^2)/((t^2-9)^{5/2)} is (t^3)/(3(t^2-9)^{5/2)}-(t^5)/(27(t^2-9)^{5/2)}+C

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integral of (t^2)/((t^2-9)^{5/2)}

\int \frac{t ^{2}}{( t ^{2} - 9 ) ^{\frac{5}{2}}} d t

\frac{t ^{3}}{3 ( t ^{2} - 9 ) ^{\frac{5}{2}}} - \frac{t ^{5}}{27 ( t ^{2} - 9 ) ^{\frac{5}{2}}} + C

Solution steps

\int \frac{t ^{2}}{( t ^{2} - 9 ) ^{\frac{5}{2}}} d t

Apply Integration By Parts

= \frac{t ^{3}}{3 ( t ^{2} - 9 ) ^{\frac{5}{2}}} - \int - \frac{5 t ^{4}}{3 ( t ^{2} - 9 ) ^{\frac{7}{2}}} d t

\int - \frac{5 t ^{4}}{3 ( t ^{2} - 9 ) ^{\frac{7}{2}}} d t = \frac{t ^{5}}{27 ( t ^{2} - 9 ) ^{\frac{5}{2}}}

= \frac{t ^{3}}{3 ( t ^{2} - 9 ) ^{\frac{5}{2}}} - \frac{t ^{5}}{27 ( t ^{2} - 9 ) ^{\frac{5}{2}}}

Add a constant to the solution

= \frac{t ^{3}}{3 ( t ^{2} - 9 ) ^{\frac{5}{2}}} - \frac{t ^{5}}{27 ( t ^{2} - 9 ) ^{\frac{5}{2}}} + C

What is the integral of (t^2)/((t^2-9)^{5/2)} ?
The integral of (t^2)/((t^2-9)^{5/2)} is (t^3)/(3(t^2-9)^{5/2)}-(t^5)/(27(t^2-9)^{5/2)}+C