What is the integral of (3x^4+x^2+2) ?

The integral of (3x^4+x^2+2) is (3x^5)/5+(x^3)/3+2x+C

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integral of (3x^4+x^2+2)

\int (3 x^{4} + x^{2} + 2) d x

\frac{3 x ^{5}}{5} + \frac{x ^{3}}{3} + 2 x + C

Solution steps

\int 3 x^{4} + x^{2} + 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 3 x^{4} d x + \int x^{2} d x + \int 2 d x

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

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

\int 2 d x = 2 x

= \frac{3 x ^{5}}{5} + \frac{x ^{3}}{3} + 2 x

Add a constant to the solution

= \frac{3 x ^{5}}{5} + \frac{x ^{3}}{3} + 2 x + C

\frac{\partial}{\partial x} (12 x^{2} y^{5} + x^{2} y^{2})

x \to 0 lim (x^{4} f (x))

\int \frac{1}{x ^{2}} (1 + \frac{1}{x})^{\frac{1}{2}} d x

2 y (x + 1) d y = x d x

\frac{1}{x ^{2}}, at 4

What is the integral of (3x^4+x^2+2) ?
The integral of (3x^4+x^2+2) is (3x^5)/5+(x^3)/3+2x+C