What is the integral of (x^3+1)/x+sin(x) ?

The integral of (x^3+1)/x+sin(x) is (x^3)/3+ln|x|-cos(x)+C

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integral of (x^3+1)/x+sin(x)

\int \frac{x ^{3} + 1}{x} + sin (x) d x

\frac{x ^{3}}{3} + ln ∣ x ∣ - cos (x) + C

Solution steps

\int \frac{x ^{3} + 1}{x} + sin (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 \frac{x ^{3} + 1}{x} d x + \int sin (x) d x

\int \frac{x ^{3} + 1}{x} d x = \frac{x ^{3}}{3} + ln ∣ x ∣

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

= \frac{x ^{3}}{3} + ln ∣ x ∣ - cos (x)

Add a constant to the solution

= \frac{x ^{3}}{3} + ln ∣ x ∣ - cos (x) + C

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