What is the integral of 1-1/2 x^4+1/24 x^8 ?

The integral of 1-1/2 x^4+1/24 x^8 is x-(x^5)/(10)+(x^9)/(216)+C

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integral of 1-1/2 x^4+1/24 x^8

\int 1 - \frac{1}{2} x^{4} + \frac{1}{24} x^{8} d x

x - \frac{x ^{5}}{10} + \frac{x ^{9}}{216} + C

Solution steps

\int 1 - \frac{1}{2} x^{4} + \frac{1}{24} x^{8} 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 1 d x - \int \frac{1}{2} x^{4} d x + \int \frac{1}{24} x^{8} d x

\int 1 d x = x

\int \frac{1}{2} x^{4} d x = \frac{x ^{5}}{10}

\int \frac{1}{24} x^{8} d x = \frac{x ^{9}}{216}

= x - \frac{x ^{5}}{10} + \frac{x ^{9}}{216}

Add a constant to the solution

= x - \frac{x ^{5}}{10} + \frac{x ^{9}}{216} + C

x \to 0 lim (x (∣ x ∣))

f (x) = \frac{6}{x}, at x = 36

x \to 2 lim (\frac{x - 2}{x ^{2} - 4})

\frac{d}{d x} (\frac{cos ( 12 x )}{e ^{7 x}})

\int \frac{sec ^{6} ( x )}{tan ^{2} ( x )} d x

What is the integral of 1-1/2 x^4+1/24 x^8 ?
The integral of 1-1/2 x^4+1/24 x^8 is x-(x^5)/(10)+(x^9)/(216)+C