What is the integral of (8x^5+3x^3-x^2+1) ?

The integral of (8x^5+3x^3-x^2+1) is (4x^6)/3+(3x^4)/4-(x^3)/3+x+C

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integral of (8x^5+3x^3-x^2+1)

\int (8 x^{5} + 3 x^{3} - x^{2} + 1) d x

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

Solution steps

\int 8 x^{5} + 3 x^{3} - x^{2} + 1 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 8 x^{5} d x + \int 3 x^{3} d x - \int x^{2} d x + \int 1 d x

\int 8 x^{5} d x = \frac{4 x ^{6}}{3}

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

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

\int 1 d x = x

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

Add a constant to the solution

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

What is the integral of (8x^5+3x^3-x^2+1) ?
The integral of (8x^5+3x^3-x^2+1) is (4x^6)/3+(3x^4)/4-(x^3)/3+x+C