What is the integral of ((1+ln(x)))/(x^3) ?

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

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integral of ((1+ln(x)))/(x^3)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int_{- 1}^{2} ∣ x ∣ d x

n = 0 \sum \infty 4^{n} + n^{4}

y = 7 x^{2} - 5 x + 2

8 x^{2} sin (x) tan (x)

\int x y cos (x y) + sin (x y) d x

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