What is the integral of (1/(x^5)-x^5-1/3) ?

The integral of (1/(x^5)-x^5-1/3) is -1/(4x^4)-(x^6)/6-1/3 x+C

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integral of (1/(x^5)-x^5-1/3)

\int (\frac{1}{x ^{5}} - x^{5} - \frac{1}{3}) d x

- \frac{1}{4 x ^{4}} - \frac{x ^{6}}{6} - \frac{1}{3} x + C

Solution steps

\int \frac{1}{x ^{5}} - x^{5} - \frac{1}{3} 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{1}{x ^{5}} d x - \int x^{5} d x - \int \frac{1}{3} d x

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

\int x^{5} d x = \frac{x ^{6}}{6}

\int \frac{1}{3} d x = \frac{1}{3} x

= - \frac{1}{4 x ^{4}} - \frac{x ^{6}}{6} - \frac{1}{3} x

Add a constant to the solution

= - \frac{1}{4 x ^{4}} - \frac{x ^{6}}{6} - \frac{1}{3} x + C

\frac{2}{1 - x ^{2}}

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 7

n = 0 \sum \infty 1 (- \frac{1}{3})^{n}

\int 56 x d x

x \to 0 lim (\frac{1}{x + 2} - \frac{1}{2})

What is the integral of (1/(x^5)-x^5-1/3) ?
The integral of (1/(x^5)-x^5-1/3) is -1/(4x^4)-(x^6)/6-1/3 x+C