What is the integral of (12x)/(sqrt(1+4)) ?

The integral of (12x)/(sqrt(1+4)) is (6x^2)/(sqrt(5))+C

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integral of (12x)/(sqrt(1+4))

\int \frac{12 x}{1 + 4} d x

\frac{6 x ^{2}}{5} + C

Solution steps

\int \frac{12 x}{1 + 4} d x

Take the constant out:

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

= \frac{12}{1 + 4} \cdot \int x d x

Simplify

= \frac{12}{5} \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{12}{5} \cdot \frac{x ^{2}}{2}

Simplify

\frac{12}{5} \cdot \frac{x ^{2}}{2} : \frac{6 x ^{2}}{5}

= \frac{6 x ^{2}}{5}

Add a constant to the solution

= \frac{6 x ^{2}}{5} + C

\int \frac{5 x}{4} d x

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What is the integral of (12x)/(sqrt(1+4)) ?
The integral of (12x)/(sqrt(1+4)) is (6x^2)/(sqrt(5))+C