What is the integral of 3x^3-5x^2+3x+4 ?

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

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integral of 3x^3-5x^2+3x+4

\int 3 x^{3} - 5 x^{2} + 3 x + 4 d x

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

Solution steps

\int 3 x^{3} - 5 x^{2} + 3 x + 4 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 5 x^{2} d x + \int 3 x d x + \int 4 d x

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

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

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