What is the integral of 5x^4-8x^3+9x^2 ?

The integral of 5x^4-8x^3+9x^2 is x^5-2x^4+3x^3+C

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integral of 5x^4-8x^3+9x^2

\int 5 x^{4} - 8 x^{3} + 9 x^{2} d x

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

Solution steps

\int 5 x^{4} - 8 x^{3} + 9 x^{2} 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 9 x^{2} d x

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

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

\int 9 x^{2} d x = 3 x^{3}

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

Add a constant to the solution

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

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

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

\int tanh (x) sech^{2} (x) d x

\int sec (t) (5 sec (t) + 7 tan (t)) d t

\int 2 1 - y^{2} d y

What is the integral of 5x^4-8x^3+9x^2 ?
The integral of 5x^4-8x^3+9x^2 is x^5-2x^4+3x^3+C