What is the integral of (3/2 x^7+12x^5-4x^3-55) ?

The integral of (3/2 x^7+12x^5-4x^3-55) is (3x^8)/(16)+2x^6-x^4-55x+C

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integral of (3/2 x^7+12x^5-4x^3-55)

\int (\frac{3}{2} x^{7} + 12 x^{5} - 4 x^{3} - 55) d x

\frac{3 x ^{8}}{16} + 2 x^{6} - x^{4} - 55 x + C

Solution steps

\int \frac{3}{2} x^{7} + 12 x^{5} - 4 x^{3} - 55 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 \frac{3}{2} x^{7} d x + \int 12 x^{5} d x - \int 4 x^{3} d x - \int 55 d x

\int \frac{3}{2} x^{7} d x = \frac{3 x ^{8}}{16}

\int 12 x^{5} d x = 2 x^{6}

\int 4 x^{3} d x = x^{4}

\int 55 d x = 55 x

= \frac{3 x ^{8}}{16} + 2 x^{6} - x^{4} - 55 x

Add a constant to the solution

= \frac{3 x ^{8}}{16} + 2 x^{6} - x^{4} - 55 x + C

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What is the integral of (3/2 x^7+12x^5-4x^3-55) ?
The integral of (3/2 x^7+12x^5-4x^3-55) is (3x^8)/(16)+2x^6-x^4-55x+C