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Popular Calculus >

integral of 12x^5

Solution

\int 12 x^{5} d x

Solution

2 x^{6} + C

Solution steps

\int 12 x^{5} d x

Take the constant out:

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

= 12 \cdot \int x^{5} d x

Apply the Power Rule

= 12 \cdot \frac{x ^{6}}{6}

Simplify

12 \cdot \frac{x ^{6}}{6} : 2 x^{6}

= 2 x^{6}

Add a constant to the solution

= 2 x^{6} + C

Graph

Popular Examples

integral from 0 to 5 of |2x-5|

\int_{0}^{5} ∣ 2 x - 5 ∣ d x

derivative of sqrt(2x+6)

\frac{d}{d x} (2 x + 6)

(\partial)/(\partial x)(4e^{xy})

\frac{\partial}{\partial x} (4 e^{x y})

area y=x,y=4,x=0,x=2sqrt(2)

a re a y = x, y = 4, x = 0, x = 22

integral of (3e^x-1/3 x^3)

\int (3 e^{x} - \frac{1}{3} x^{3}) d x

Frequently Asked Questions (FAQ)

What is the integral of 12x^5 ?
The integral of 12x^5 is 2x^6+C