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

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

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

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

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

Solution steps

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

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

\int (x^{3}) d x

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

\int \frac{1}{x ^{\frac{1}{3}} + x ^{\frac{1}{2}}} d x

x + 1 \frac{d y}{d x} + (x + 2) y = 2 x e^{- x}

\int_{0}^{x} 1 + t^{2} d t

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