What is the integral of 1+2sin(x)+3/(sqrt(x)) ?

The integral of 1+2sin(x)+3/(sqrt(x)) is x-2cos(x)+6sqrt(x)+C

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integral of 1+2sin(x)+3/(sqrt(x))

\int 1 + 2 sin (x) + \frac{3}{x} d x

x - 2 cos (x) + 6 x + C

Solution steps

\int 1 + 2 sin (x) + \frac{3}{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 1 d x + \int 2 sin (x) d x + \int \frac{3}{x} d x

\int 1 d x = x

\int 2 sin (x) d x = - 2 cos (x)

\int \frac{3}{x} d x = 6 x

= x - 2 cos (x) + 6 x

Add a constant to the solution

= x - 2 cos (x) + 6 x + C

(1 + x y) d x + x^{2} d y = 0

3 y d x = 2 x d y

\int - sin (x) tan (x) d x

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

\frac{8 - x e ^{x}}{x + e ^{x}}

What is the integral of 1+2sin(x)+3/(sqrt(x)) ?
The integral of 1+2sin(x)+3/(sqrt(x)) is x-2cos(x)+6sqrt(x)+C