What is the integral of (2e^x+sec(x)tan(x)-sqrt(x)) ?

The integral of (2e^x+sec(x)tan(x)-sqrt(x)) is 2e^x+sec(x)-2/3 x^{3/2}+C

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integral of (2e^x+sec(x)tan(x)-sqrt(x))

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

What is the integral of (2e^x+sec(x)tan(x)-sqrt(x)) ?
The integral of (2e^x+sec(x)tan(x)-sqrt(x)) is 2e^x+sec(x)-2/3 x^{3/2}+C