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Popular >

integral of (x^5-6x)

Solution

\int (x^{5} - 6 x) d x

Solution

\frac{x ^{6}}{6} - 3 x^{2} + C

Solution steps

\int x^{5} - 6 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{5} d x - \int 6 x d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 6 x d x = 3 x^{2}

= \frac{x ^{6}}{6} - 3 x^{2}

Add a constant to the solution

= \frac{x ^{6}}{6} - 3 x^{2} + C

Popular Examples

y^{''}-10y^'+25y=t^{-5}e^{5t}

y^{^{''}} - 10 y^{^{'}} + 25 y = t^{- 5} e^{5 t}

derivative of x/(x^2-4)derivative of

\frac{x}{x ^{2} - 4}

d/(dθ)(1/(2cos(θ)+3sin(θ)))

\frac{d}{d θ} (\frac{1}{2 cos ( θ ) + 3 sin ( θ )})

derivative of sin(sin(2x))

\frac{d}{d x} (sin (sin (2 x)))

\int - 2 d x

Frequently Asked Questions (FAQ)

What is the integral of (x^5-6x) ?
The integral of (x^5-6x) is (x^6)/6-3x^2+C