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

The integral of f((tan(1))/x)^2 is (tan^2(1)}{x^2}*\frac{f^2)/2+C

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

integral

f (\frac{tan ( 1 )}{x})^{2}

\frac{tan ^{2} ( 1 )}{x ^{2}} \cdot \frac{f ^{2}}{2} + C

Solution steps

\int f (\frac{tan ( 1 )}{x})^{2} df

Take the constant out:

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

= (\frac{tan ( 1 )}{x})^{2} \cdot \int fdf

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{tan ^{2} ( 1 )}{x ^{2}} \cdot \int fdf

Apply the Power Rule

: \frac{f ^{2}}{2}

= \frac{tan ^{2} ( 1 )}{x ^{2}} \cdot \frac{f ^{2}}{2}

Add a constant to the solution

= \frac{tan ^{2} ( 1 )}{x ^{2}} \cdot \frac{f ^{2}}{2} + C

3 x^{- 4}

\frac{1}{( x ^{2} + c )}

(cos (x))^{3}

\frac{x ^{2}}{( x ^{2} + 1 ) ^{2}}

4 - x \cdot 2

What is the integral of f((tan(1))/x)^2 ?
The integral of f((tan(1))/x)^2 is (tan^2(1)}{x^2}*\frac{f^2)/2+C