What is the integral of 5x^4-8x^5 ?

The integral of 5x^4-8x^5 is x^5-(4x^6)/3+C

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integral of 5x^4-8x^5

\int 5 x^{4} - 8 x^{5} d x

x^{5} - \frac{4 x ^{6}}{3} + C

Solution steps

\int 5 x^{4} - 8 x^{5} 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 8 x^{5} d x

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

\int 8 x^{5} d x = \frac{4 x ^{6}}{3}

= x^{5} - \frac{4 x ^{6}}{3}

Add a constant to the solution

= x^{5} - \frac{4 x ^{6}}{3} + C

y^{^{''}} = a \cdot y

(x^{2} - 6 x + 10) 25 - x^{2}

4 sec (x) tan (x)

y^{^{'}} = 3 x + y, y (0) = 3

\frac{d}{d x} (3 x sin (2 x))