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

The integral of (12x^4-5x^3-7) is (12x^5)/5-(5x^4)/4-7x+C

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integral of (12x^4-5x^3-7)

\int (12 x^{4} - 5 x^{3} - 7) d x

\frac{12 x ^{5}}{5} - \frac{5 x ^{4}}{4} - 7 x + C

Solution steps

\int 12 x^{4} - 5 x^{3} - 7 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 12 x^{4} d x - \int 5 x^{3} d x - \int 7 d x

\int 12 x^{4} d x = \frac{12 x ^{5}}{5}

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

\int 7 d x = 7 x

= \frac{12 x ^{5}}{5} - \frac{5 x ^{4}}{4} - 7 x

Add a constant to the solution

= \frac{12 x ^{5}}{5} - \frac{5 x ^{4}}{4} - 7 x + C

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