What is the integral of (5x^4+3x^2+6) ?

The integral of (5x^4+3x^2+6) is x^5+x^3+6x+C

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integral of (5x^4+3x^2+6)

\int (5 x^{4} + 3 x^{2} + 6) d x

x^{5} + x^{3} + 6 x + C

Solution steps

\int 5 x^{4} + 3 x^{2} + 6 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 5 x^{4} d x + \int 3 x^{2} d x + \int 6 d x

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

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

\int 6 d x = 6 x

= x^{5} + x^{3} + 6 x

Add a constant to the solution

= x^{5} + x^{3} + 6 x + C

\int \frac{2 x}{5 x ^{2} + 1} d x

\int \frac{1 + 3 x ^{2}}{x ^{2} ( 1 + x ^{2} )} d x

\int c^{a x} d x

\int \frac{5}{x \cdot x ^{5} + 4} d x

\int \frac{8 x + 6}{( 4 x ^{2} + 6 x ) ^{3}} d x

What is the integral of (5x^4+3x^2+6) ?
The integral of (5x^4+3x^2+6) is x^5+x^3+6x+C