What is the integral of (3x^2+4x+e^x+sec(x)tan(x)) ?

The integral of (3x^2+4x+e^x+sec(x)tan(x)) is x^3+2x^2+e^x+sec(x)+C

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integral of (3x^2+4x+e^x+sec(x)tan(x))

\int (3 x^{2} + 4 x + e^{x} + sec (x) tan (x)) d x

x^{3} + 2 x^{2} + e^{x} + sec (x) + C

Solution steps

\int 3 x^{2} + 4 x + e^{x} + sec (x) tan (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 3 x^{2} d x + \int 4 x d x + \int e^{x} d x + \int sec (x) tan (x) d x

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

\int 4 x d x = 2 x^{2}

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

\int sec (x) tan (x) d x = sec (x)

= x^{3} + 2 x^{2} + e^{x} + sec (x)

Add a constant to the solution

= x^{3} + 2 x^{2} + e^{x} + sec (x) + C

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What is the integral of (3x^2+4x+e^x+sec(x)tan(x)) ?
The integral of (3x^2+4x+e^x+sec(x)tan(x)) is x^3+2x^2+e^x+sec(x)+C