What is the integral of (x^{17}+3e^x-cos(x)+1/x) ?

The integral of (x^{17}+3e^x-cos(x)+1/x) is (x^{18})/(18)+3e^x-sin(x)+ln|x|+C

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integral of (x^{17}+3e^x-cos(x)+1/x)

\int (x^{17} + 3 e^{x} - cos (x) + \frac{1}{x}) d x

\frac{x ^{18}}{18} + 3 e^{x} - sin (x) + ln ∣ x ∣ + C

Solution steps

\int x^{17} + 3 e^{x} - cos (x) + \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 x^{17} d x + \int 3 e^{x} d x - \int cos (x) d x + \int \frac{1}{x} d x

\int x^{17} d x = \frac{x ^{18}}{18}

\int 3 e^{x} d x = 3 e^{x}

\int cos (x) d x = sin (x)

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{18}}{18} + 3 e^{x} - sin (x) + ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{18}}{18} + 3 e^{x} - sin (x) + ln ∣ x ∣ + C

f (x) = x^{- 6}

\frac{\partial}{\partial x} (\frac{1}{1 - \frac{5}{x}})

\int (e^{t} + 2 t + ln (t)) d t

y^{^{'}} = 5 y (1 - \frac{y}{7})

\frac{d}{d s} (1)

What is the integral of (x^{17}+3e^x-cos(x)+1/x) ?
The integral of (x^{17}+3e^x-cos(x)+1/x) is (x^{18})/(18)+3e^x-sin(x)+ln|x|+C