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

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

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

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

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

Solution steps

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

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

\int e^{x} d x = e^{x}

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

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

Simplify

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

Add a constant to the solution

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

(3 x)^{^{'}}

\int 4 tan^{2} (x) sec^{2} (x) d x

y = 3 x, y = \frac{5}{7} x, y = 54 - x^{2}

\int arcsin (\frac{1}{x}) d x

f (x) = 8.8 x

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