What is the integral of (2x^3-x^2+3x-7) ?

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

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integral of (2x^3-x^2+3x-7)

\int (2 x^{3} - x^{2} + 3 x - 7) d x

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

Solution steps

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

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

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

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

\int 7 d x = 7 x

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

Add a constant to the solution

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

\int_{0}^{2} 5 d x

\int \frac{1}{7 x ^{7}} d x

\frac{d}{d x} (sin (4 x) + 2 x^{\frac{3}{2}})

sin (x), x = \frac{π}{4}

\frac{d}{d x} ((ln (x)) d x)

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