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Popular >

integral of (6x^2)

Solution

\int (6 x^{2}) d x

Solution

2 x^{3} + C

Solution steps

\int 6 x^{2} d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= 6 \cdot \frac{x ^{3}}{3}

Simplify

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

= 2 x^{3}

Add a constant to the solution

= 2 x^{3} + C

Popular Examples

derivative of (x^2+3/(cos(x)))

\frac{d}{d x} (\frac{x ^{2} + 3}{cos ( x )})

tangent of y=arctan(x/4),(4, pi/4)tangent of

y = arctan (\frac{x}{4}), (4, \frac{π}{4})

(\partial)/(\partial x)(x^5y)

\frac{\partial}{\partial x} (x^{5} y)

integral of (4x^2+2x+8)/(x(x^2+2)^2)

\int \frac{4 x ^{2} + 2 x + 8}{x ( x ^{2} + 2 ) ^{2}} d x

limit as x approaches+1 of-3/(x-1)

x \to + 1 lim (- \frac{3}{x - 1})

Frequently Asked Questions (FAQ)

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