What is the integral of 0.04x+27 ?

The integral of 0.04x+27 is 12.5(0.04x+27)^2+C

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integral of 0.04x+27

\int 0.04 x + 27 d x

12.5 (0.04 x + 27)^{2} + C

Solution steps

\int 0.04 x + 27 d x

Apply u-substitution

: \int \frac{u}{0.04} d u

= \int \frac{u}{0.04} d u

Take the constant out:

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

= \frac{1}{0.04} \cdot \int u d u

Simplify

= 25 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 25 \cdot \frac{u ^{2}}{2}

Substitute back

u = 0.04 x + 27

= 25 \cdot \frac{( 0.04 x + 27 ) ^{2}}{2}

Simplify

25 \cdot \frac{( 0.04 x + 27 ) ^{2}}{2} : 12.5 (0.04 x + 27)^{2}

= 12.5 (0.04 x + 27)^{2}

Add a constant to the solution

= 12.5 (0.04 x + 27)^{2} + C

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What is the integral of 0.04x+27 ?
The integral of 0.04x+27 is 12.5(0.04x+27)^2+C