What is the integral of (5x^3-7x^2+2x+1) ?

The integral of (5x^3-7x^2+2x+1) is (5x^4)/4-(7x^3)/3+x^2+x+C

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integral of (5x^3-7x^2+2x+1)

\int (5 x^{3} - 7 x^{2} + 2 x + 1) d x

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

Solution steps

\int 5 x^{3} - 7 x^{2} + 2 x + 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 5 x^{3} d x - \int 7 x^{2} d x + \int 2 x d x + \int 1 d x

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

\frac{d}{d x} (30 + \frac{1}{x + 1} - 3 x^{2})

\frac{d}{d x} (\frac{1}{5 x ^{2} + 2 x})

\frac{5 s + 3}{( s - 1 ) ( s ^{2} + 2 s + 5 )}

\frac{\partial}{\partial y} (x^{2} + e^{x y})

y = csc^{1} (e^{8 t})

What is the integral of (5x^3-7x^2+2x+1) ?
The integral of (5x^3-7x^2+2x+1) is (5x^4)/4-(7x^3)/3+x^2+x+C