What is the integral of (7x^4+x^2+3) ?

The integral of (7x^4+x^2+3) is (7x^5)/5+(x^3)/3+3x+C

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integral of (7x^4+x^2+3)

\int (7 x^{4} + x^{2} + 3) d x

\frac{7 x ^{5}}{5} + \frac{x ^{3}}{3} + 3 x + C

Solution steps

\int 7 x^{4} + x^{2} + 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 7 x^{4} d x + \int x^{2} d x + \int 3 d x

\int 7 x^{4} d x = \frac{7 x ^{5}}{5}

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

\int 3 d x = 3 x

= \frac{7 x ^{5}}{5} + \frac{x ^{3}}{3} + 3 x

Add a constant to the solution

= \frac{7 x ^{5}}{5} + \frac{x ^{3}}{3} + 3 x + C

\int x e^{- x} - x^{2} d x

\int - \frac{x}{x ^{2} + 1} d x

\int 2 + sec^{2} (x) d x

\int 7 - x^{2} d x

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

What is the integral of (7x^4+x^2+3) ?
The integral of (7x^4+x^2+3) is (7x^5)/5+(x^3)/3+3x+C