What is the integral of (12)/(sqrt(x))+12sqrt(x) ?

The integral of (12)/(sqrt(x))+12sqrt(x) is 24sqrt(x)+8x^{3/2}+C

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integral of (12)/(sqrt(x))+12sqrt(x)

\int \frac{12}{x} + 12 x d x

24 x + 8 x^{\frac{3}{2}} + C

Solution steps

\int \frac{12}{x} + 12 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 \frac{12}{x} d x + \int 12 x d x

\int \frac{12}{x} d x = 24 x

\int 12 x d x = 8 x^{\frac{3}{2}}

= 24 x + 8 x^{\frac{3}{2}}

Add a constant to the solution

= 24 x + 8 x^{\frac{3}{2}} + C

y = \frac{1}{x ^{2}}, y = 9, x = 8

\frac{d}{d x} (arcsec (2^{x}))

f (x) = 5 tan (x), at x = \frac{π}{4}

5

\frac{d}{d x} (9 x - 45)

What is the integral of (12)/(sqrt(x))+12sqrt(x) ?
The integral of (12)/(sqrt(x))+12sqrt(x) is 24sqrt(x)+8x^{3/2}+C