Question: "Find the general indefinite integral. (Use C for..."

Barbara Schroder

Answered question

2021-11-22

Find the general indefinite integral. (Use C for the constant of integration.)

\int (u^{6} - 2 u^{5} - u^{3} + \frac{4}{3}) d u

Theirl1972

Beginner2021-11-23Added 22 answers

Step 1
Find the general indefinite integral.
Given:

\int (u^{6} - 2 u^{5} - u^{3} + \frac{4}{3}) d u

Apply the power rule,

\int (x^{n}) d x = \frac{x^{n + 1}}{n + 1}, n \neq - 1

Integral of constant,

\int a d x = a x

Step 2
Now integrate the term, we get

\Rightarrow [\frac{u^{6 + 1}}{6 + 1} - 2 \frac{u^{5 + 1}}{5 + 1} - \frac{u^{3 + 1}}{3 + 1} + \frac{4}{3} u] + C

\Rightarrow \frac{u^{7}}{7} - 2 \frac{u^{6}}{6} - \frac{u^{4}}{4} + \frac{4}{3} u + C

Margaret Plemons

Beginner2021-11-24Added 13 answers

Step 1: Expand.

\int u^{6} - 2 u^{5} - u^{3} + \frac{4}{3} d u

Step 2: Use Power Rule:

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

\frac{u^{7}}{7} - \frac{u^{6}}{3} - \frac{u^{4}}{4} + \frac{4 u}{3}

Step 3: Add constant.

\frac{u^{7}}{7} - \frac{u^{6}}{3} - \frac{u^{4}}{4} + \frac{4 u}{3} + C

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