What is the integral of 0.8x+3 ?

The integral of 0.8x+3 is 0.625(0.8x+3)^2+C

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integral of 0.8x+3

\int 0.8 x + 3 d x

0.625 (0.8 x + 3)^{2} + C

Solution steps

\int 0.8 x + 3 d x

Apply u-substitution

: \int \frac{u}{0.8} d u

= \int \frac{u}{0.8} d u

Take the constant out:

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

= \frac{1}{0.8} \cdot \int u d u

Simplify

= 1.25 \cdot \int u d u

Apply the Power Rule

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

= 1.25 \cdot \frac{u ^{2}}{2}

Substitute back

u = 0.8 x + 3

= 1.25 \cdot \frac{( 0.8 x + 3 ) ^{2}}{2}

Simplify

1.25 \cdot \frac{( 0.8 x + 3 ) ^{2}}{2} : 0.625 (0.8 x + 3)^{2}

= 0.625 (0.8 x + 3)^{2}

Add a constant to the solution

= 0.625 (0.8 x + 3)^{2} + C

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