What is the integral of e^x-1/x+4+5x^3 ?

The integral of e^x-1/x+4+5x^3 is e^x-ln|x|+4x+(5x^4)/4+C

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integral of e^x-1/x+4+5x^3

\int e^{x} - \frac{1}{x} + 4 + 5 x^{3} d x

e^{x} - ln ∣ x ∣ + 4 x + \frac{5 x ^{4}}{4} + C

Solution steps

\int e^{x} - \frac{1}{x} + 4 + 5 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 e^{x} d x - \int \frac{1}{x} d x + \int 4 d x + \int 5 x^{3} d x

\int e^{x} d x = e^{x}

\int \frac{1}{x} d x = ln ∣ x ∣

\int 4 d x = 4 x

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

= e^{x} - ln ∣ x ∣ + 4 x + \frac{5 x ^{4}}{4}

Add a constant to the solution

= e^{x} - ln ∣ x ∣ + 4 x + \frac{5 x ^{4}}{4} + C

\int \frac{v ^{2}}{- v ^{2} + 3} d v

\int sin (3 x + 4) d x

\frac{d}{d x} (\frac{2}{( x - 3 t ) ^{2} + 1})

x \to 1 lim (x (x - 2))

x \to 0 + lim (x)

What is the integral of e^x-1/x+4+5x^3 ?
The integral of e^x-1/x+4+5x^3 is e^x-ln|x|+4x+(5x^4)/4+C