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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (a^{2} - x^{2})

y = 5 x + 2

k = 3 \sum \infty \frac{3}{k ^{2} - 2 k}

(5 x + 7)^{2}

\int sin (4 t) cos (4 t) d t

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