What is the integral of 2sqrt((4-t^2)/(t^8)) ?

The integral of 2sqrt((4-t^2)/(t^8)) is 2(-(sqrt(4-t^2))/(3t^3)+(sqrt(4-t^2))/(12t))+C

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integral of 2sqrt((4-t^2)/(t^8))

\int 2 \frac{4 - t ^{2}}{t ^{8}} d t

2 (- \frac{4 - t ^{2}}{3 t ^{3}} + \frac{4 - t ^{2}}{12 t}) + C

Solution steps

\int 2 \frac{4 - t ^{2}}{t ^{8}} d t

Take the constant out:

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

= 2 \cdot \int \frac{4 - t ^{2}}{t ^{8}} d t

Simplify

\frac{4 - t ^{2}}{t ^{8}} : \frac{4 - t ^{2}}{t ^{4}}

= 2 \cdot \int \frac{4 - t ^{2}}{t ^{4}} d t

Apply Integration By Parts

: - \frac{4 - t ^{2}}{3 t ^{3}} - \int \frac{1}{3 t ^{2} - t ^{2} + 4} d t

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

\int \frac{1}{3 t ^{2} - t ^{2} + 4} d t = - \frac{4 - t ^{2}}{12 t}

= 2 (- \frac{4 - t ^{2}}{3 t ^{3}} - (- \frac{4 - t ^{2}}{12 t}))

Simplify

= 2 (- \frac{4 - t ^{2}}{3 t ^{3}} + \frac{4 - t ^{2}}{12 t})

Add a constant to the solution

= 2 (- \frac{4 - t ^{2}}{3 t ^{3}} + \frac{4 - t ^{2}}{12 t}) + C

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What is the integral of 2sqrt((4-t^2)/(t^8)) ?
The integral of 2sqrt((4-t^2)/(t^8)) is 2(-(sqrt(4-t^2))/(3t^3)+(sqrt(4-t^2))/(12t))+C