Expert Answer to "Determine the following indefinite integral. ∫(x8−3x3+1)dx"

pamangking8

Answered question

2021-11-16

Determine the following indefinite integral.

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

Richard Cheatham

Beginner2021-11-17Added 16 answers

Step 1
First we separate the integral.

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

= \int x^{8} d x - 3 \int x^{3} d x + \int d x

Step 2
Then we integrate each part

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

= \int x^{8} d x - 3 \int x^{3} d x + \int d x

= \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

Xyle1991

Beginner2021-11-18Added 15 answers

Step 1: Expand.

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

Step 2: Use Power Rule:

\int x^{n} d x = \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

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?