What is the integral of (x+1)^{-1/2}-pi*cos(pix) ?

The integral of (x+1)^{-1/2}-pi*cos(pix) is 2(x+1)^{1/2}-sin(pix)+C

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integral of (x+1)^{-1/2}-pi*cos(pix)

\int (x + 1)^{- \frac{1}{2}} - π \cdot cos (π x) d x

2 (x + 1)^{\frac{1}{2}} - sin (π x) + C

Solution steps

\int (x + 1)^{- \frac{1}{2}} - π cos (π 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 + 1)^{- \frac{1}{2}} d x - \int π cos (π x) d x

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

\int π cos (π x) d x = sin (π x)

= 2 (x + 1)^{\frac{1}{2}} - sin (π x)

Add a constant to the solution

= 2 (x + 1)^{\frac{1}{2}} - sin (π x) + C

What is the integral of (x+1)^{-1/2}-pi*cos(pix) ?
The integral of (x+1)^{-1/2}-pi*cos(pix) is 2(x+1)^{1/2}-sin(pix)+C