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

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

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integral of e^x-3x^2+sin(x)

\int e^{x} - 3 x^{2} + sin (x) d x

e^{x} - x^{3} - cos (x) + C

Solution steps

\int e^{x} - 3 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 e^{x} d x - \int 3 x^{2} d x + \int sin (x) d x

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

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

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

= e^{x} - x^{3} - cos (x)

Add a constant to the solution

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

\int e^{t} - 3 d t

\int e^{- \frac{x}{6}} d x

\int e^{5 x - 1} d x

\int (3 x^{4} - 4 x^{3} - x - 4) d x

\int (5 x + 4) d x

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