What is the integral of (5x^2-3)(2x) ?

The integral of (5x^2-3)(2x) is 1/10 (5x^2-3)^2+C

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integral of (5x^2-3)(2x)

\int (5 x^{2} - 3) (2 x) d x

\frac{1}{10} (5 x^{2} - 3)^{2} + C

Solution steps

\int (5 x^{2} - 3) \cdot 2 x d x

Take the constant out:

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

= 2 \cdot \int (5 x^{2} - 3) x d x

Apply u-substitution

: \int \frac{u}{10} d u

= 2 \cdot \int \frac{u}{10} d u

Take the constant out:

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

= 2 \cdot \frac{1}{10} \cdot \int u d u

Apply the Power Rule

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

= 2 \cdot \frac{1}{10} \cdot \frac{u ^{2}}{2}

Substitute back

u = 5 x^{2} - 3

= 2 \cdot \frac{1}{10} \cdot \frac{( 5 x ^{2} - 3 ) ^{2}}{2}

Simplify

2 \cdot \frac{1}{10} \cdot \frac{( 5 x ^{2} - 3 ) ^{2}}{2} : \frac{1}{10} (5 x^{2} - 3)^{2}

= \frac{1}{10} (5 x^{2} - 3)^{2}

Add a constant to the solution

= \frac{1}{10} (5 x^{2} - 3)^{2} + C

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What is the integral of (5x^2-3)(2x) ?
The integral of (5x^2-3)(2x) is 1/10 (5x^2-3)^2+C