What is the integral of x/(sqrt(4+x^2)) ?

The integral of x/(sqrt(4+x^2)) is sqrt(4+x^2)+C

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integral of x/(sqrt(4+x^2))

\int \frac{x}{4 + x ^{2}} d x

4 + x^{2} + C

Solution steps

\int \frac{x}{4 + x ^{2}} d x

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 4 + x^{2}

= \frac{1}{2} \cdot 2 (4 + x^{2})^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (4 + x^{2})^{\frac{1}{2}} : 4 + x^{2}

= 4 + x^{2}

Add a constant to the solution

= 4 + x^{2} + C

\frac{x ^{5} + e ^{x}}{x + 2}

f (x) = 4 x^{\frac{1}{2}} + 8 x^{\frac{3}{2}} + 9, at x = 4

\int_{e}^{\infty} x^{0} ln (x) d x

\frac{( 2 s + 2 )}{( s + 10 )}

\int \frac{1}{P ( a - b P )} d P

What is the integral of x/(sqrt(4+x^2)) ?
The integral of x/(sqrt(4+x^2)) is sqrt(4+x^2)+C