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

The integral of 1/(2x+1)+1/(sqrt(1-x)) is 1/2 ln|2x+1|-2sqrt(1-x)+C

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integral of 1/(2x+1)+1/(sqrt(1-x))

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

\frac{1}{2} ln ∣ 2 x + 1 ∣ - 2 1 - x + C

Solution steps

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

\int \frac{1}{2 x + 1} d x = \frac{1}{2} ln ∣ 2 x + 1 ∣

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

= \frac{1}{2} ln ∣ 2 x + 1 ∣ - 2 1 - x

Add a constant to the solution

= \frac{1}{2} ln ∣ 2 x + 1 ∣ - 2 1 - x + C

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

\int sin^{3} (4 x) cos^{3} (4 x) d x

y^{^{'}} = (2 x + y)^{2}

y^{^{''}} + 7 y + 10 = 0, y (0) = 3, y^{^{'}} (0) = 18

\frac{d}{d s} (\frac{6 s ^{3} + 28 s ^{2} + 38 s + 15}{( s + 1 ) ^{2}})

What is the integral of 1/(2x+1)+1/(sqrt(1-x)) ?
The integral of 1/(2x+1)+1/(sqrt(1-x)) is 1/2 ln|2x+1|-2sqrt(1-x)+C