What is the integral of (3+x)/(x^{2023)} ?

The integral of (3+x)/(x^{2023)} is -1/(674x^{2022)}-1/(2021x^{2021)}+C

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integral of (3+x)/(x^{2023)}

\int \frac{3 + x}{x ^{2023}} d x

- \frac{1}{674 x ^{2022}} - \frac{1}{2021 x ^{2021}} + C

Solution steps

\int \frac{3 + x}{x ^{2023}} d x

Expand

\frac{3 + x}{x ^{2023}} : \frac{3}{x ^{2023}} + \frac{1}{x ^{2022}}

= \int \frac{3}{x ^{2023}} + \frac{1}{x ^{2022}} 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{3}{x ^{2023}} d x + \int \frac{1}{x ^{2022}} d x

\int \frac{3}{x ^{2023}} d x = - \frac{1}{674 x ^{2022}}

\int \frac{1}{x ^{2022}} d x = - \frac{1}{2021 x ^{2021}}

= - \frac{1}{674 x ^{2022}} - \frac{1}{2021 x ^{2021}}

Add a constant to the solution

= - \frac{1}{674 x ^{2022}} - \frac{1}{2021 x ^{2021}} + C

x + 1

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

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What is the integral of (3+x)/(x^{2023)} ?
The integral of (3+x)/(x^{2023)} is -1/(674x^{2022)}-1/(2021x^{2021)}+C