A calculus problem by A Former Brilliant Member

Calculus Level 1

Evaluate the indefinite integral ∫ 3 x 4 d x . \large \int 3x^4 \, dx .


Notation: C C denotes the arbitrary constant of integration .

3 4 x 4 + C \frac{3}{4}x^4 + C 3 5 x 5 + C \frac{3}{5}x^5 + C x 5 + C x^5 + C 5 3 x 5 + C \frac{5}{3}x^5 + C

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

By Power Rule.

∫ x n d x = x ( n + 1 ) n + 1 + C \large\int x^ndx= \dfrac{x^{(n+1)}}{n+1} + C

Applying the formula, we have

∫ 3 x 4 d x = 3 ∫ x 4 d x = 3 x 5 5 + C = 3 5 x 5 + C \large\int 3x^4dx=3\int x^4dx=\frac{3x^5}{5} + C = \frac{3}{5}x^5 + C

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Hunter Edwards
Nov 10, 2017

Use the power rule: ∫ x n d x = x n + 1 ( n + 1 ) \int_ {}^{} x^{n}dx= \frac{x^{n+1}}{(n+1)}

Then, plug in our numbers, and we have:

∫ 3 x 4 d x = 3 x 4 + 1 ( 4 + 1 ) + C = 3 x 5 5 + C \int_ {}^{} 3x^{4}dx= \frac{3x^{4+1}}{(4+1)}+C= \frac{3x^{5}}{5}+C

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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