What is the integral of ((16-t^2)^{3/2})/(t^6) ?

The integral of ((16-t^2)^{3/2})/(t^6) is -((16-t^2)^{3/2})/(5t^5)+((16-t^2)^{3/2})/(80t^3)+C

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integral of ((16-t^2)^{3/2})/(t^6)

\int \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{t ^{6}} d t

- \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{5 t ^{5}} + \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{80 t ^{3}} + C

Solution steps

\int \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{t ^{6}} d t

Apply Integration By Parts

= - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{5 t ^{5}} - \int \frac{3 ( - t ^{2} + 16 ) ^{\frac{1}{2}}}{5 t ^{4}} d t

\int \frac{3 ( - t ^{2} + 16 ) ^{\frac{1}{2}}}{5 t ^{4}} d t = - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{80 t ^{3}}

= - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{5 t ^{5}} - - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{80 t ^{3}}

Simplify

= - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{5 t ^{5}} + \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{80 t ^{3}}

Add a constant to the solution

= - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{5 t ^{5}} + \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{80 t ^{3}} + C

What is the integral of ((16-t^2)^{3/2})/(t^6) ?
The integral of ((16-t^2)^{3/2})/(t^6) is -((16-t^2)^{3/2})/(5t^5)+((16-t^2)^{3/2})/(80t^3)+C