What is the integral of x/(sqrt(16+x^2)) ?

The integral of x/(sqrt(16+x^2)) is sqrt(16+x^2)+C

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integral of x/(sqrt(16+x^2))

\int \frac{x}{16 + x ^{2}} d x

16 + x^{2} + C

Solution steps

\int \frac{x}{16 + 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 = 16 + x^{2}

= \frac{1}{2} \cdot 2 (16 + x^{2})^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (16 + x^{2})^{\frac{1}{2}} : 16 + x^{2}

= 16 + x^{2}

Add a constant to the solution

= 16 + x^{2} + C

x \to 3 lim (2 x + ∣ x - 3 ∣)

x \to 7 lim (\frac{x + 5}{x + 9})

x^{2} y^{^{''}} + x y^{^{'}} + 9 y = 10 x

y = x^{3} + 2

\int tan^{3} (6 x) d x

What is the integral of x/(sqrt(16+x^2)) ?
The integral of x/(sqrt(16+x^2)) is sqrt(16+x^2)+C