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Popular >

integral of (-5x)

Solution

\int (- 5 x) d x

Solution

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

Solution steps

\int - 5 x d x

Take the constant out:

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

= - 5 \cdot \int x d x

Apply the Power Rule

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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

Popular Examples

integral of (x+1/2)^6

\int (x + \frac{1}{2})^{6} d x

integral of (2u)/(sqrt(-4u^2+9))

\int \frac{2 u}{- 4 u ^{2} + 9} d u

integral of 1/((x^2+1)(x^2+1))

\int \frac{1}{( x ^{2} + 1 ) ( x ^{2} + 1 )} d x

integral of (6x+5)/(x^2-20x+101)

\int \frac{6 x + 5}{x ^{2} - 20 x + 101} d x

integral of (x^2)/3 sec^2(x^3-3)

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

Frequently Asked Questions (FAQ)

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