What is the integral of (2/(x^3)+sqrt(x^4)) ?

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

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integral of (2/(x^3)+sqrt(x^4))

\int (\frac{2}{x ^{3}} + x^{4}) d x

- \frac{1}{x ^{2}} + \frac{x ^{3}}{3} + C

Solution steps

\int \frac{2}{x ^{3}} + 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{2}{x ^{3}} d x + \int x^{4} d x

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

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

= - \frac{1}{x ^{2}} + \frac{x ^{3}}{3}

Add a constant to the solution

= - \frac{1}{x ^{2}} + \frac{x ^{3}}{3} + C

\frac{d}{d x} (ln (tan (2 x)))

\frac{\partial}{\partial t} (1 - cos (t))

\frac{d}{d x} (\frac{8}{x ^{7}})

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

\int_{0}^{1} t^{3} (1 + t^{4})^{3} d t

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