What is the integral of x^5-sec(x)+1/(2sqrt(x)) ?

The integral of x^5-sec(x)+1/(2sqrt(x)) is (x^6)/6-ln|tan(x)+sec(x)|+sqrt(x)+C

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integral of x^5-sec(x)+1/(2sqrt(x))

\int x^{5} - sec (x) + \frac{1}{2 x} d x

\frac{x ^{6}}{6} - ln ∣ tan (x) + sec (x) ∣ + x + C

Solution steps

\int x^{5} - sec (x) + \frac{1}{2 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 x^{5} d x - \int sec (x) d x + \int \frac{1}{2 x} d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

\int \frac{1}{2 x} d x = x

= \frac{x ^{6}}{6} - ln ∣ tan (x) + sec (x) ∣ + x

Add a constant to the solution

= \frac{x ^{6}}{6} - ln ∣ tan (x) + sec (x) ∣ + x + C

\int x I n^{2} x d x

\frac{( s + 3 )}{( s + 1 ) ( s + 2 )}

\int e^{x} - sin (x) d x

e^{0.42 x}

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

What is the integral of x^5-sec(x)+1/(2sqrt(x)) ?
The integral of x^5-sec(x)+1/(2sqrt(x)) is (x^6)/6-ln|tan(x)+sec(x)|+sqrt(x)+C