What is the integral of e^x+2sec^2(x)+4/x+sqrt(x) ?

The integral of e^x+2sec^2(x)+4/x+sqrt(x) is e^x+2tan(x)+4ln|x|+2/3 x^{3/2}+C

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integral of e^x+2sec^2(x)+4/x+sqrt(x)

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

e^{x} + 2 tan (x) + 4 ln ∣ x ∣ + \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

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

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

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

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

= e^{x} + 2 tan (x) + 4 ln ∣ x ∣ + \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= e^{x} + 2 tan (x) + 4 ln ∣ x ∣ + \frac{2}{3} x^{\frac{3}{2}} + C

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What is the integral of e^x+2sec^2(x)+4/x+sqrt(x) ?
The integral of e^x+2sec^2(x)+4/x+sqrt(x) is e^x+2tan(x)+4ln|x|+2/3 x^{3/2}+C