What is the antiderivative of $f (x) = \frac{1}{2} + (\frac{3}{4}) x^{2} - (\frac{4}{5}) x^{3}$ $f(x) = 1/2 + (3/4)x^2 - (4/5)x^3$ ?

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Answer 1 · 2017-02-15T20:30:37

$\int f (x) = \frac{1}{2} x + \frac{1}{4} x^{3} - \frac{1}{5} x^{4} + C$ $intf(x)=1/2x+1/4x^3-1/5x^4+"C"$

Integrating this function is trivial using the power rule:

$\int a x^{n} = \frac{a x^{n + 1}}{n + 1} + C$ $intax^n=(ax^(n+1))/(n+1)+"C"$

What is the antiderivative of f(x) = 1/2 + (3/4)x^2 - (4/5)x^3f(x)=12+(34)x2−(45)x3f(x) = 1/2 + (3/4)x^2 - (4/5)x^3?