en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 2x-6x^3

Solution

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

Solution

x^{2} - \frac{3 x ^{4}}{2} + C

Solution steps

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

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

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

= x^{2} - \frac{3 x ^{4}}{2}

Add a constant to the solution

= x^{2} - \frac{3 x ^{4}}{2} + C

Graph

Popular Examples

derivative of 2pi-xcos(x)

\frac{d}{d x} (2 π - x cos (x))

cos^2(x)sin(x)(dy)/(dx)cos^3(x)y=1

cos^{2} (x) sin (x) \frac{d y}{d x} cos^{3} (x) y = 1

laplacetransform \H(t-2pi)sin(t-2pi)

l a pl a ce t r an s f or m H (t - 2 π) sin (t - 2 π)

derivative of (2+x/((2-x)^5))

\frac{d}{d x} (\frac{2 + x}{( 2 - x ) ^{5}})

integral from 1 to 5 of M/(e^M)

\int_{1}^{5} \frac{M}{e ^{M}} d M

Frequently Asked Questions (FAQ)

What is the integral of 2x-6x^3 ?
The integral of 2x-6x^3 is x^2-(3x^4)/2+C