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Popular >

integral of 3x^2+x

Solution

\int 3 x^{2} + x d x

Solution

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

Solution steps

\int 3 x^{2} + x 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 3 x^{2} d x + \int x d x

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

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

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

Add a constant to the solution

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

Popular Examples

limit as x approaches 10-of 1/((x-10)^2)

x \to 10 - lim (\frac{1}{( x - 10 ) ^{2}})

derivative of f(x)=e^θsin(6θ)derivative of

f (x) = e^{θ} sin (6 θ)

limit as x approaches 2 of 3x^2-x+5

x \to 2 lim (3 x^{2} - x + 5)

(\partial)/(\partial x)(-5x^2-5y^2+xy)

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

yy^'=3((y^2-2)/(x^3))x^2

y y^{^{'}} = 3 (\frac{y ^{2} - 2}{x ^{3}}) x^{2}

Frequently Asked Questions (FAQ)

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