What is the integral of (1/(x^4)-x^4-1/4) ?

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

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integral of (1/(x^4)-x^4-1/4)

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

- \frac{1}{3 x ^{3}} - \frac{x ^{5}}{5} - \frac{1}{4} x + C

Solution steps

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

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

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

\int \frac{1}{4} d x = \frac{1}{4} x

= - \frac{1}{3 x ^{3}} - \frac{x ^{5}}{5} - \frac{1}{4} x

Add a constant to the solution

= - \frac{1}{3 x ^{3}} - \frac{x ^{5}}{5} - \frac{1}{4} x + C

\int cos (2 x) \cdot sin (2 x) d x

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

n = 0 \sum \infty \frac{1}{n ( n + 1 )}

\frac{d}{d x} (arctan (\frac{x - y}{x}))

576 π - 4 π^{3} x^{2} + 4 π x^{2}

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