What is the integral of x^2+sin(x)+1 ?

The integral of x^2+sin(x)+1 is (x^3)/3-cos(x)+x+C

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integral of x^2+sin(x)+1

\int x^{2} + sin (x) + 1 d x

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

Solution steps

\int x^{2} + sin (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^{2} d x + \int sin (x) d x + \int 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

x \to - \infty lim (\frac{8 x ^{3}}{9 x ^{4}})

\int - cos (x) 2 x d x

x^{2} + \frac{16}{x}

\frac{d}{d x} (\frac{x - 5}{3 x - 4})

\frac{d}{d x} (- \frac{ln ( 2 )}{x ( x + ln ( 2 ) )})

What is the integral of x^2+sin(x)+1 ?
The integral of x^2+sin(x)+1 is (x^3)/3-cos(x)+x+C