Expert answers to "Determine the following indefinite integral. ∫(3x5−5x9)dx"

erurnSopSoypegx

Answered question

2021-11-18

Determine the following indefinite integral.

\int (3 x^{5} - 5 x^{9}) d x

pseudoenergy34

Beginner2021-11-19Added 22 answers

Step 1
Given integral is:

I = \int (3 x^{5} - 5 x^{9}) d x

Integrating we get,

I = \int 3 x^{5} d x - \int 5 x^{9} d x + c

I = 3 (\frac{x^{6}}{5 + 1}) - 5 (\frac{x^{10}}{9 + 1}) + c

I = 3 (\frac{x^{6}}{6}) - 5 (\frac{x^{10}}{10}) + c

I = \frac{x^{6}}{2} - \frac{x^{10}}{2} + c

where c is the constant of integration.
Step 2
Differentiating I with respect to x we get,

d \frac{I}{d x} = (\frac{d}{d x}) [\frac{x^{6}}{2} - \frac{x^{10}}{2} + c]

d \frac{I}{d x} = \frac{6 x^{5}}{2} - \frac{10 x^{9}}{2} + 0

d \frac{I}{d x} = 3 x^{5} - 5 x^{9}

which is the integrand of the given integral.

George Morin

Beginner2021-11-20Added 13 answers

Step 1: Expand.

\int 3 x^{5} - 5 x^{9} d x

Step 2: Use Power Rule:

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

\frac{x^{6}}{2} - \frac{x^{10}}{2}

Step 3: Add constant.

\frac{x^{6}}{2} - \frac{x^{10}}{2} + C

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