What is the integral of 4/(x^5)-5x^4 ?

The integral of 4/(x^5)-5x^4 is -1/(x^4)-x^5+C

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integral of 4/(x^5)-5x^4

\int \frac{4}{x ^{5}} - 5 x^{4} d x

- \frac{1}{x ^{4}} - x^{5} + C

Solution steps

\int \frac{4}{x ^{5}} - 5 x^{4} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{4}{x ^{5}} d x - \int 5 x^{4} d x

\int \frac{4}{x ^{5}} d x = - \frac{1}{x ^{4}}

\int 5 x^{4} d x = x^{5}

= - \frac{1}{x ^{4}} - x^{5}

Add a constant to the solution

= - \frac{1}{x ^{4}} - x^{5} + C

\frac{\partial}{\partial y} (ln (x^{6} y))

n = 0 \sum \infty (\frac{2}{3})^{n}

\frac{d}{d x} (- \frac{x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}})

\frac{d ^{2}}{d x ^{2}} (e^{x^{2} + 1})

\frac{d}{d x} (x ln^{3} (x))

What is the integral of 4/(x^5)-5x^4 ?
The integral of 4/(x^5)-5x^4 is -1/(x^4)-x^5+C