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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

x \to 0 lim (\frac{2 ( y + x ) - 2 y}{x})

\int 6 x^{2} + 4 x - 1 d x

\int \frac{10 x ^{3} - 5 x}{x ^{4} - x ^{2} + 6} d x

\int 3 x \cdot e^{x} d x

\int \frac{( e ^{x} )}{1 - e ^{2 x}} d x

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