We have an answer to "Evaluate the following integrals. ∫x3−1x2dx"

ambiguit

Answered question

2021-11-19

Evaluate the following integrals.

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

Answer & Explanation

mylouscrapza

Beginner2021-11-20Added 22 answers

Step 1
Given,

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

To solve the above integral.
Step 2
Now,

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

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

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

; {Since,

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

}

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

Befoodly

Beginner2021-11-21Added 17 answers

Step 1: Simplify

\frac{x^{3} - 1}{x^{2}} \to x - \frac{1}{x^{2}}

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

Step 3: Use Power Rule:

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

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

Step 4: Use Power Rule:

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

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

Step 5: Add constant.

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

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