What is the integral of 1/((2x^2)^2) ?

The integral of 1/((2x^2)^2) is -1/(12x^3)+C

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integral of 1/((2x^2)^2)

\int \frac{1}{( 2 x ^{2} ) ^{2}} d x

- \frac{1}{12 x ^{3}} + C

Solution steps

\int \frac{1}{( 2 x ^{2} ) ^{2}} d x

Simplify

\frac{1}{( 2 x ^{2} ) ^{2}} : \frac{1}{4 x ^{4}}

= \int \frac{1}{4 x ^{4}} d x

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{1}{x ^{4}} d x

Apply the Power Rule

= \frac{1}{4} (- \frac{1}{3 x ^{3}})

Simplify

\frac{1}{4} (- \frac{1}{3 x ^{3}}) : - \frac{1}{12 x ^{3}}

= - \frac{1}{12 x ^{3}}

Add a constant to the solution

= - \frac{1}{12 x ^{3}} + C

\int e^{- a x} cos (x) d x

\int x e^{- 3} d x

\int sin^{4} (\frac{t}{2}) d t

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

\int (x^{\frac{3}{2}} + 12 x + 2) d x

What is the integral of 1/((2x^2)^2) ?
The integral of 1/((2x^2)^2) is -1/(12x^3)+C