Get the solution to "Evaluate this indefinite integral: ∫(6x5−18x2+7)dx"

postillan4

Answered question

2021-11-06

Evaluate this indefinite integral:

\int (6 x^{5} - 18 x^{2} + 7) d x

tabuordg

Skilled2021-11-07Added 99 answers

Step 1
We have to evaluate the indefinite integral:

\int (6 x^{5} - 18 x^{2} + 7) d x

We know the formula of integration,

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

(C is an arbitrary constant)

\int d x = x + C

\int a x^{n} d x = a \int x^{n} d x

(where a is some constant)
Step 2
Applying above formula for the given indefinite integration, we get

\int (6 x^{5} - 18 x^{2} + 7) d x = 6 \int x^{5} d x - 18 \int x^{2} d x + 7 \int d x

= 6 \times \frac{x^{5 + 1}}{5 + 1} - 18 \times \frac{x^{2 + 1}}{2 + 1} + 7 x + C

= 6 \times \frac{x^{6}}{6} - 18 \times \frac{x^{3}}{3} + 7 x + C

= x^{6} - 6 x^{3} + 7 x + C

Hence, value of indefinite integration is

x^{6} - 6 x^{3} + 7 x + C

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