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

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

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

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

\frac{x ^{3}}{3} + sin (x) + C

Solution steps

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

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

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

= \frac{x ^{3}}{3} + sin (x)

Add a constant to the solution

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

\int cos (y) sin (y) + y^{2} d y

\int 4 cos (5 x) d x

\frac{1}{x ^{2} + 1}

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\int \frac{1}{x ^{2}} sin (\frac{6}{x}) cos (\frac{6}{x}) d x

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