What is the integral of 3tan(x)sec(x)+4x^{1/2} ?

The integral of 3tan(x)sec(x)+4x^{1/2} is 3sec(x)+8/3 x^{3/2}+C

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integral of 3tan(x)sec(x)+4x^{1/2}

\int 3 tan (x) sec (x) + 4 x^{\frac{1}{2}} d x

3 sec (x) + \frac{8}{3} x^{\frac{3}{2}} + C

Solution steps

\int 3 tan (x) sec (x) + 4 x^{\frac{1}{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 3 tan (x) sec (x) d x + \int 4 x^{\frac{1}{2}} d x

\int 3 tan (x) sec (x) d x = 3 sec (x)

\int 4 x^{\frac{1}{2}} d x = \frac{8}{3} x^{\frac{3}{2}}

= 3 sec (x) + \frac{8}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 3 sec (x) + \frac{8}{3} x^{\frac{3}{2}} + C

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What is the integral of 3tan(x)sec(x)+4x^{1/2} ?
The integral of 3tan(x)sec(x)+4x^{1/2} is 3sec(x)+8/3 x^{3/2}+C