What is the integral of 3x^3-2x^2+8x-6 ?

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

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integral of 3x^3-2x^2+8x-6

\int 3 x^{3} - 2 x^{2} + 8 x - 6 d x

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

Solution steps

\int 3 x^{3} - 2 x^{2} + 8 x - 6 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^{3} d x - \int 2 x^{2} d x + \int 8 x d x - \int 6 d x

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

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

\int 8 x d x = 4 x^{2}

\int 6 d x = 6 x

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

Add a constant to the solution

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

\int 2 a 1 + cos (θ) d θ

\frac{d}{d x} (cos (x) - \frac{1}{3} cos^{3} (x))

\int \frac{x - 5}{- 2 x + 2} d x

\int x n (\frac{1}{x}) d x

\int_{0}^{1} e^{x^{2}} d x

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