What is the integral of 20x^3+1/x ?

The integral of 20x^3+1/x is 5x^4+ln|x|+C

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integral of 20x^3+1/x

\int 20 x^{3} + \frac{1}{x} d x

5 x^{4} + ln ∣ x ∣ + C

Solution steps

\int 20 x^{3} + \frac{1}{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 20 x^{3} d x + \int \frac{1}{x} d x

\int 20 x^{3} d x = 5 x^{4}

\int \frac{1}{x} d x = ln ∣ x ∣

= 5 x^{4} + ln ∣ x ∣

Add a constant to the solution

= 5 x^{4} + ln ∣ x ∣ + C

\frac{2 x}{6 x - 5}

x \to 0 lim (e^{- x^{2}})

\frac{d y}{d x} = \frac{x - 1}{y - 3}

y = \frac{5}{3}, y = \frac{1}{4 - x ^{2}}

\frac{d}{d t} (2 + t)