Cynthia Bell

2021-12-27

Evaluate the indefinite integral.

$\int \frac{3}{x}+\frac{2}{5{x}^{6}}dx$

censoratojk

Beginner2021-12-28Added 46 answers

Step 1

This question is based on indefinite integral.

General form,

Integral of$x}^{n$ is $\frac{{x}^{(x+1)}}{n+1}$

As for x = 1 formula violates because result comes is not defined.

Therefore, integral of 1/x is$\mathrm{ln}\left(x\right)$

Step 2

Given

$\int (\frac{3}{x}+\frac{2}{5{x}^{6}})dx$

$=\int \frac{3}{x}dx+\int \frac{2}{5{x}^{6}}dx\text{}\text{}\text{}\because \int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}$ and $\int \frac{1}{x}dx=\mathrm{ln}\left(x\right)$

$=3\mathrm{ln}\left(x\right)+\frac{2}{5}\frac{{x}^{(-6+1)}}{(-6+1)}+C$

$=3\mathrm{ln}\left(x\right)+\frac{2}{5}\frac{{x}^{-5}}{-5}+C$

$=3\mathrm{ln}\left(x\right)-\frac{2}{25}{x}^{-5}+C$

Hence, Answer is$3\mathrm{ln}\left(x\right)-\frac{2}{25}{x}^{-5}+C$

This question is based on indefinite integral.

General form,

Integral of

As for x = 1 formula violates because result comes is not defined.

Therefore, integral of 1/x is

Step 2

Given

Hence, Answer is

Foreckije

Beginner2021-12-29Added 32 answers

Lets

karton

Expert2022-01-04Added 613 answers

Given:

Use properties of integrals

Evaluate the integrals

Add C

Answer:

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