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 (2 + tan^{2} (x))^{2} d x

\int cos (x) cos (5 sin (x)) d x

\int sec (2) (x) tan (2) (x) d x

\int 1 - \frac{1}{x ^{2}} \frac{1}{x ^{3}} d x

\int \frac{2 z - 3}{z ^{2} - 6 z + 13} d z

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