What is the integral of 1/(sqrt(x)tan(\sqrt{x)+2)} ?

The integral of 1/(sqrt(x)tan(\sqrt{x)+2)} is 2cot(2)sqrt(x)+C

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integral of 1/(sqrt(x)tan(\sqrt{x)+2)}

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

2 cot (2) x + C

Solution steps

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

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

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

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: 2 x^{\frac{1}{2}}

= \frac{1}{tan ( 2 )} \cdot 2 x^{\frac{1}{2}}

Simplify

\frac{1}{tan ( 2 )} \cdot 2 x^{\frac{1}{2}} : 2 cot (2) x

= 2 cot (2) x

Add a constant to the solution

= 2 cot (2) x + C

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What is the integral of 1/(sqrt(x)tan(\sqrt{x)+2)} ?
The integral of 1/(sqrt(x)tan(\sqrt{x)+2)} is 2cot(2)sqrt(x)+C