What is the integral of (ln(x^2))/(x^4) ?

The integral of (ln(x^2))/(x^4) is -(2ln(x))/(3x^3)-2/(9x^3)+C

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integral of (ln(x^2))/(x^4)

\int \frac{ln ( x ^{2} )}{x ^{4}} d x

- \frac{2 ln ( x )}{3 x ^{3}} - \frac{2}{9 x ^{3}} + C

Solution steps

\int \frac{ln ( x ^{2} )}{x ^{4}} d x

Apply Integration By Parts

: - \frac{ln ( x ^{2} )}{3 x ^{3}} - \int - \frac{2}{3 x ^{4}} d x

= - \frac{ln ( x ^{2} )}{3 x ^{3}} - \int - \frac{2}{3 x ^{4}} d x

\int - \frac{2}{3 x ^{4}} d x = \frac{2}{9 x ^{3}}

= - \frac{ln ( x ^{2} )}{3 x ^{3}} - \frac{2}{9 x ^{3}}

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= - \frac{2 ln ( x )}{3 x ^{3}} - \frac{2}{9 x ^{3}}

Add a constant to the solution

= - \frac{2 ln ( x )}{3 x ^{3}} - \frac{2}{9 x ^{3}} + C

\int \frac{( x ^{3} + 1 )}{x ^{4} + 4 x} d x

2

\int 3^{u} d u

\int \frac{2 sin ( x ) - 5 cos ( x )}{cos ( x )} d x

\int (sec (x) (sec (x) + tan (x))) d x

What is the integral of (ln(x^2))/(x^4) ?
The integral of (ln(x^2))/(x^4) is -(2ln(x))/(3x^3)-2/(9x^3)+C