"Find the indefinite integral ∫(1x2−x3)" solved and explained

totalmente80sm9

Answered question

2021-11-19

Find the indefinite integral

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

Tionant

Beginner2021-11-20Added 17 answers

Step 1
Given Data
The integral function is

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

.
Write the integral function in individual integral,

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

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

Step 2
Solve the above integral,

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

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

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

Here C is constant.
Thus the indefinite integral

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

memomzungup4

Beginner2021-11-21Added 14 answers

Step 1: Expand.

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

Step 2: Use Sum Rule:

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

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

Step 3: Use Power Rule:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

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

Step 4: Use Power Rule:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

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

Step 5: Add constant.

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

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