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Popular >

integral of x+12x^2

Solution

\int x + 12 x^{2} d x

Solution

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

Solution steps

\int x + 12 x^{2} 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 x d x + \int 12 x^{2} d x

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

\int 12 x^{2} d x = 4 x^{3}

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

Add a constant to the solution

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

Popular Examples

f(x)=(x-2)^2(x-3)^3

f (x) = (x - 2)^{2} (x - 3)^{3}

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

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

implicit (dy)/(dx),sqrt(xy)=x^7y+72 implicit derivative

\frac{d y}{d x}, x y = x^{7} y + 72

limit as x approaches-infinity of ln(x-2)

x \to - \infty lim (ln (x - 2))

derivative of y=(tan(1/x))^{sec(1/x)}derivative of

y = (tan (\frac{1}{x}))^{s e c (\frac{1}{x})}

Frequently Asked Questions (FAQ)

What is the integral of x+12x^2 ?
The integral of x+12x^2 is (x^2)/2+4x^3+C