What is the integral of (ln(t))/(t^3) ?

The integral of (ln(t))/(t^3) is -(ln(t))/(2t^2)-1/(4t^2)+C

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integral of (ln(t))/(t^3)

\int \frac{ln ( t )}{t ^{3}} d t

- \frac{ln ( t )}{2 t ^{2}} - \frac{1}{4 t ^{2}} + C

Solution steps

\int \frac{ln ( t )}{t ^{3}} d t

Apply Integration By Parts

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

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

= - \frac{ln ( t )}{2 t ^{2}} - \frac{1}{4 t ^{2}}

Add a constant to the solution

= - \frac{ln ( t )}{2 t ^{2}} - \frac{1}{4 t ^{2}} + C

x \to 3 - lim (\frac{2}{x ^{2} - 9})

d er i v a t i v e e^{9 - x}

y^{^{''}} + 25 y = cos (6 t)

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

\int \frac{5 x ^{2}}{( x - 1 ) ( x ^{2} + 9 )} d x

What is the integral of (ln(t))/(t^3) ?
The integral of (ln(t))/(t^3) is -(ln(t))/(2t^2)-1/(4t^2)+C