Determine the following indefinite integral.

$\int ({x}^{8}-3{x}^{3}+1)dx$

pamangking8
2021-11-16
Answered

Determine the following indefinite integral.

$\int ({x}^{8}-3{x}^{3}+1)dx$

You can still ask an expert for help

Richard Cheatham

Answered 2021-11-17
Author has **16** answers

Step 1

First we separate the integral.

$\int ({x}^{8}-3{x}^{3}+1)dx$

$=\int {x}^{8}dx-3\int {x}^{3}dx+\int dx$

Step 2

Then we integrate each part

$\int ({x}^{8}-3{x}^{3}+1)dx$

$=\int {x}^{8}dx-3\int {x}^{3}dx+\int dx$

$=\frac{{x}^{9}}{9}-3\frac{{x}^{4}}{4}+x+C$

$=\frac{{x}^{9}}{9}-\frac{3{x}^{4}}{4}+x+C$

Answer:$\frac{{x}^{9}}{9}-\frac{3{x}^{4}}{4}+x+C$

C=integrating constant

First we separate the integral.

Step 2

Then we integrate each part

Answer:

C=integrating constant

Xyle1991

Answered 2021-11-18
Author has **15** answers

Step 1: Expand.

$\int ({x}^{8}-3{x}^{3}+1)dx$

Step 2: Use Power Rule:$\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+C$ .

$\frac{{x}^{9}}{9}-\frac{3{x}^{4}}{4}+x$

Step 3: Add constant.

$\frac{{x}^{9}}{9}-\frac{3{x}^{4}}{4}+x+C$

Step 2: Use Power Rule:

Step 3: Add constant.

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