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Popular >

integral of 3r^3

Solution

\int 3 r^{3} d r

Solution

\frac{3 r ^{4}}{4} + C

Solution steps

\int 3 r^{3} d r

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int r^{3} d r

Apply the Power Rule

: \frac{r ^{4}}{4}

= 3 \cdot \frac{r ^{4}}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 r ^{4}}{4}

Add a constant to the solution

= \frac{3 r ^{4}}{4} + C

Popular Examples

integral of 1/(10+x)

\int \frac{1}{10 + x} d x

integral of ((x^2+x))/(x(x-1)^2)

\int \frac{( x ^{2} + x )}{x ( x - 1 ) ^{2}} d x

integral of cos(2/3)x

\int cos (\frac{2}{3}) x d x

integral of ((2x+5))/(x^2-4x+7)

\int \frac{( 2 x + 5 )}{x ^{2} - 4 x + 7} d x

integral of (4x^3)/(x^4)

\int \frac{4 x ^{3}}{x ^{4}} d x

Frequently Asked Questions (FAQ)

What is the integral of 3r^3 ?
The integral of 3r^3 is (3r^4)/4+C