What is the integral of ((x^2)/2+sin(x)) ?

The integral of ((x^2)/2+sin(x)) is (x^3)/6-cos(x)+C

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integral of ((x^2)/2+sin(x))

\int (\frac{x ^{2}}{2} + sin (x)) d x

\frac{x ^{3}}{6} - cos (x) + C

Solution steps

\int \frac{x ^{2}}{2} + 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 ^{2}}{2} d x + \int sin (x) d x

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

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

= \frac{x ^{3}}{6} - cos (x)

Add a constant to the solution

= \frac{x ^{3}}{6} - cos (x) + C

What is the integral of ((x^2)/2+sin(x)) ?
The integral of ((x^2)/2+sin(x)) is (x^3)/6-cos(x)+C