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Popular >

integral of 8t^5

Solution

\int 8 t^{5} d t

Solution

\frac{4 t ^{6}}{3} + C

Solution steps

\int 8 t^{5} d t

Take the constant out:

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

= 8 \cdot \int t^{5} d t

Apply the Power Rule

: \frac{t ^{6}}{6}

= 8 \cdot \frac{t ^{6}}{6}

Simplify

8 \cdot \frac{t ^{6}}{6} : \frac{4 t ^{6}}{3}

= \frac{4 t ^{6}}{3}

Add a constant to the solution

= \frac{4 t ^{6}}{3} + C

Popular Examples

derivative of axcos(x+bxsin(x))

\frac{d}{d x} (a x cos (x) + b x sin (x))

implicit (dy)/(dx),y^4=x^7 implicit derivative

\frac{d y}{d x}, y^{4} = x^{7}

sec^2(pi/4)(pi/5)= 1/4 (dx)/(dt)

sec^{2} (\frac{π}{4}) (\frac{π}{5}) = \frac{1}{4} \frac{d x}{d t}

limit as x approaches 6+of sqrt(6-x)

x \to 6 + lim (6 - x)

(\partial)/(\partial x)((x^2+y^2)^{4/5})

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{\frac{4}{5}})

Frequently Asked Questions (FAQ)

What is the integral of 8t^5 ?
The integral of 8t^5 is (4t^6)/3+C