What is the integral of (12x^7+25x^6-22x^5+15x^4) ?

The integral of (12x^7+25x^6-22x^5+15x^4) is (3x^8)/2+(25x^7)/7-(11x^6)/3+3x^5+C

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integral of (12x^7+25x^6-22x^5+15x^4)

\int (12 x^{7} + 25 x^{6} - 22 x^{5} + 15 x^{4}) d x

\frac{3 x ^{8}}{2} + \frac{25 x ^{7}}{7} - \frac{11 x ^{6}}{3} + 3 x^{5} + C

Solution steps

\int 12 x^{7} + 25 x^{6} - 22 x^{5} + 15 x^{4} 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^{7} d x + \int 25 x^{6} d x - \int 22 x^{5} d x + \int 15 x^{4} d x

\int 12 x^{7} d x = \frac{3 x ^{8}}{2}

\int 25 x^{6} d x = \frac{25 x ^{7}}{7}

\int 22 x^{5} d x = \frac{11 x ^{6}}{3}

\int 15 x^{4} d x = 3 x^{5}

= \frac{3 x ^{8}}{2} + \frac{25 x ^{7}}{7} - \frac{11 x ^{6}}{3} + 3 x^{5}

Add a constant to the solution

= \frac{3 x ^{8}}{2} + \frac{25 x ^{7}}{7} - \frac{11 x ^{6}}{3} + 3 x^{5} + C

What is the integral of (12x^7+25x^6-22x^5+15x^4) ?
The integral of (12x^7+25x^6-22x^5+15x^4) is (3x^8)/2+(25x^7)/7-(11x^6)/3+3x^5+C