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

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

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

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

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

Solution steps

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

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

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

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

= - sin (x) + e^{x} + x^{3}

Add a constant to the solution

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

\int \frac{2 x ^{2}}{1 + 1 - x ^{2}} d x

\int \frac{1}{a ^{x}} d x

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

\int sec (\frac{x}{9}) d x

\int cos (x) ln (tan (x)) d x

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