What is the integral of (5x^4-8x^3+6x-3) ?

The integral of (5x^4-8x^3+6x-3) is x^5-2x^4+3x^2-3x+C

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integral of (5x^4-8x^3+6x-3)

\int (5 x^{4} - 8 x^{3} + 6 x - 3) d x

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

Solution steps

\int 5 x^{4} - 8 x^{3} + 6 x - 3 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^{4} d x - \int 8 x^{3} d x + \int 6 x d x - \int 3 d x

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

\int 8 x^{3} d x = 2 x^{4}

\int 6 x d x = 3 x^{2}

\int 3 d x = 3 x

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

Add a constant to the solution

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

\int \frac{1}{x \cdot x ^{2} - 4} d x

\int \frac{w ^{3}}{w ^{4} - 5} d w

\int \frac{4 x - 5}{x ^{2} - 4 x + 8} d x

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

\int 5 x^{2} e^{5 x} d x

What is the integral of (5x^4-8x^3+6x-3) ?
The integral of (5x^4-8x^3+6x-3) is x^5-2x^4+3x^2-3x+C