What is the integral of (sqrt(x)-cos(+e^x+4)) ?

The integral of (sqrt(x)-cos(+e^x+4)) is 2/3 x^{3/2}-cos(4)\Ci(e^x)+sin(4)\Si(e^x)+C

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integral of (sqrt(x)-cos(+e^x+4))

\int (x - cos (+ e^{x} + 4)) d x

\frac{2}{3} x^{\frac{3}{2}} - cos (4) Ci (e^{x}) + sin (4) Si (e^{x}) + C

Solution steps

\int x - cos (e^{x} + 4) d x

Rewrite using trig identities

= \int x - cos (4) cos (e^{x}) + sin (4) sin (e^{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 d x - \int cos (4) cos (e^{x}) d x + \int sin (4) sin (e^{x}) d x

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

\int cos (4) cos (e^{x}) d x = cos (4) Ci (e^{x})

\int sin (4) sin (e^{x}) d x = sin (4) Si (e^{x})

= \frac{2}{3} x^{\frac{3}{2}} - cos (4) Ci (e^{x}) + sin (4) Si (e^{x})

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} - cos (4) Ci (e^{x}) + sin (4) Si (e^{x}) + C

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What is the integral of (sqrt(x)-cos(+e^x+4)) ?
The integral of (sqrt(x)-cos(+e^x+4)) is 2/3 x^{3/2}-cos(4)\Ci(e^x)+sin(4)\Si(e^x)+C