What is the integral of 3x^5+7x^2-6x^3+2x+5 ?

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

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integral of 3x^5+7x^2-6x^3+2x+5

\int 3 x^{5} + 7 x^{2} - 6 x^{3} + 2 x + 5 d x

\frac{x ^{6}}{2} + \frac{7 x ^{3}}{3} - \frac{3 x ^{4}}{2} + x^{2} + 5 x + C

Solution steps

\int 3 x^{5} + 7 x^{2} - 6 x^{3} + 2 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 3 x^{5} d x + \int 7 x^{2} d x - \int 6 x^{3} d x + \int 2 x d x + \int 5 d x

\int 3 x^{5} d x = \frac{x ^{6}}{2}

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

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

\int 2 x d x = x^{2}

\int 5 d x = 5 x

= \frac{x ^{6}}{2} + \frac{7 x ^{3}}{3} - \frac{3 x ^{4}}{2} + x^{2} + 5 x

Add a constant to the solution

= \frac{x ^{6}}{2} + \frac{7 x ^{3}}{3} - \frac{3 x ^{4}}{2} + x^{2} + 5 x + C

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