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Popular >

integral of 1/5 x

Solution

\int \frac{1}{5} x d x

Solution

\frac{x ^{2}}{10} + C

Solution steps

\int \frac{1}{5} x d x

Take the constant out:

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

= \frac{1}{5} \cdot \int x d x

Apply the Power Rule

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

= \frac{1}{5} \cdot \frac{x ^{2}}{2}

Simplify

\frac{1}{5} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{10}

= \frac{x ^{2}}{10}

Add a constant to the solution

= \frac{x ^{2}}{10} + C

Popular Examples

integral of 2/(x^3sqrt(x^4-81))

\int \frac{2}{x ^{3} x ^{4} - 81} d x

d/(dt)(e^{-at}cos(wt))

\frac{d}{d t} (e^{- a t} cos (wt))

integral of (x^22^x+x)/(x^2)

\int \frac{x ^{2} 2 ^{x} + x}{x ^{2}} d x

derivative of ((3x^2+1^3)/((2x^2-1)^4))

\frac{d}{d x} (\frac{( 3 x ^{2} + 1 ) ^{3}}{( 2 x ^{2} - 1 ) ^{4}})

f^{^{'}} (x) = a^{2 x}

Frequently Asked Questions (FAQ)

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