What is the integral of (7ln(x))/(x^4) ?

The integral of (7ln(x))/(x^4) is 7(-(ln(x))/(3x^3)-1/(9x^3))+C

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integral of (7ln(x))/(x^4)

\int \frac{7 ln ( x )}{x ^{4}} d x

7 (- \frac{ln ( x )}{3 x ^{3}} - \frac{1}{9 x ^{3}}) + C

Solution steps

\int \frac{7 ln ( x )}{x ^{4}} d x

Take the constant out:

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

= 7 \cdot \int \frac{ln ( x )}{x ^{4}} d x

Apply Integration By Parts

: - \frac{ln ( x )}{3 x ^{3}} - \int - \frac{1}{3 x ^{4}} d x

= 7 (- \frac{ln ( x )}{3 x ^{3}} - \int - \frac{1}{3 x ^{4}} d x)

\int - \frac{1}{3 x ^{4}} d x = \frac{1}{9 x ^{3}}

= 7 (- \frac{ln ( x )}{3 x ^{3}} - \frac{1}{9 x ^{3}})

Add a constant to the solution

= 7 (- \frac{ln ( x )}{3 x ^{3}} - \frac{1}{9 x ^{3}}) + C

n = 1 \sum \infty n^{2} e^{- n^{2}}

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

\int \frac{1}{p - z} + \frac{1}{z} d z

\int 4 (x - 1) d x

\frac{x ^{6}}{2 - x ^{5}}

What is the integral of (7ln(x))/(x^4) ?
The integral of (7ln(x))/(x^4) is 7(-(ln(x))/(3x^3)-1/(9x^3))+C