What is the integral of x^3*cos(x^4+2)+x^{-1} ?

The integral of x^3*cos(x^4+2)+x^{-1} is 1/4 sin(x^4+2)+ln|x|+C

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integral of x^3*cos(x^4+2)+x^{-1}

\int x^{3} \cdot cos (x^{4} + 2) + x^{- 1} d x

\frac{1}{4} sin (x^{4} + 2) + ln ∣ x ∣ + C

Solution steps

\int x^{3} cos (x^{4} + 2) + x^{- 1} 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^{3} cos (x^{4} + 2) d x + \int x^{- 1} d x

\int x^{3} cos (x^{4} + 2) d x = \frac{1}{4} sin (x^{4} + 2)

\int x^{- 1} d x = ln ∣ x ∣

= \frac{1}{4} sin (x^{4} + 2) + ln ∣ x ∣

Add a constant to the solution

= \frac{1}{4} sin (x^{4} + 2) + ln ∣ x ∣ + C

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What is the integral of x^3*cos(x^4+2)+x^{-1} ?
The integral of x^3*cos(x^4+2)+x^{-1} is 1/4 sin(x^4+2)+ln|x|+C