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Popular Calculus >

integral of sh x/3

Solution

\int s h \frac{x}{3} d x

Solution

\frac{h s x ^{2}}{6} + C

Solution steps

\int s h \frac{x}{3} d x

Take the constant out:

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

= \frac{1}{3} h s \cdot \int x d x

Simplify

\frac{1}{3} h s : \frac{h s}{3}

= \frac{h s}{3} \cdot \int x d x

Apply the Power Rule

= \frac{h s}{3} \cdot \frac{x ^{2}}{2}

Simplify

\frac{h s}{3} \cdot \frac{x ^{2}}{2} : \frac{h s x ^{2}}{6}

= \frac{h s x ^{2}}{6}

Add a constant to the solution

= \frac{h s x ^{2}}{6} + C

Graph

Popular Examples

integral of 29arctan(sqrt(x))

\int 29 arctan (x) d x

derivative of e^{2x-3}

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

tangent of f(x)=x-5sin(x),\at x= pi/2

t an g e n t f (x) = x - 5 sin (x), at x = \frac{π}{2}

limit as x approaches-7+of (x+6)/(x+7)

x \to - 7 + lim (\frac{x + 6}{x + 7})

integral of x/(sqrt(x^2+7))

\int \frac{x}{x ^{2} + 7} d x

Frequently Asked Questions (FAQ)

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