What is the integral of-(f(x))^2 ?

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

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integral of-(f(x))^2

integral

- (f (x))^{2}

- x^{2} f^{3} + \frac{2 x ^{2} f ^{3}}{3} + C

Solution steps

\int - (f x)^{2} df

Take the constant out:

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

= - \int (x f)^{2} df

Apply Integration By Parts

: x^{2} f^{3} - \int 2 x^{2} f^{2} df

= - (x^{2} f^{3} - \int 2 x^{2} f^{2} df)

\int 2 x^{2} f^{2} df = \frac{2 x ^{2} f ^{3}}{3}

= - (x^{2} f^{3} - \frac{2 x ^{2} f ^{3}}{3})

Simplify

= - x^{2} f^{3} + \frac{2 x ^{2} f ^{3}}{3}

Add a constant to the solution

= - x^{2} f^{3} + \frac{2 x ^{2} f ^{3}}{3} + C

\frac{( x ^{4} )}{( x ^{5} + x )}

y = \frac{4}{( 5 - 3 x )}

x (tan (x))^{2}

x^{2} + 2

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

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