What is the integral of 9.8x+10 ?

The integral of 9.8x+10 is 0.05102…(9.8x+10)^2+C

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integral of 9.8x+10

\int 9.8 x + 10 d x

0.05102 \dots (9.8 x + 10)^{2} + C

Solution steps

\int 9.8 x + 10 d x

Apply u-substitution

: \int \frac{u}{9.8} d u

= \int \frac{u}{9.8} d u

Take the constant out:

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

= \frac{1}{9.8} \cdot \int u d u

Simplify

= 0.10204 \dots \cdot \int u d u

Apply the Power Rule

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

= 0.10204 \dots \cdot \frac{u ^{2}}{2}

Substitute back

u = 9.8 x + 10

= 0.10204 \dots \cdot \frac{( 9.8 x + 10 ) ^{2}}{2}

Simplify

0.10204 \dots \cdot \frac{( 9.8 x + 10 ) ^{2}}{2} : 0.05102 \dots (9.8 x + 10)^{2}

= 0.05102 \dots (9.8 x + 10)^{2}

Add a constant to the solution

= 0.05102 \dots (9.8 x + 10)^{2} + C

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What is the integral of 9.8x+10 ?
The integral of 9.8x+10 is 0.05102…(9.8x+10)^2+C