What is the integral of (11x)/(sqrt(x^2+1)) ?

The integral of (11x)/(sqrt(x^2+1)) is 11sqrt(x^2+1)+C

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integral of (11x)/(sqrt(x^2+1))

\int \frac{11 x}{x ^{2} + 1} d x

11 x^{2} + 1 + C

Solution steps

\int \frac{11 x}{x ^{2} + 1} d x

Take the constant out:

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

= 11 \cdot \int \frac{x}{x ^{2} + 1} d x

Apply u-substitution

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

= 11 \cdot \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

= 11 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= 11 \cdot \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = x^{2} + 1

= 11 \cdot \frac{1}{2} \cdot 2 (x^{2} + 1)^{\frac{1}{2}}

Simplify

11 \cdot \frac{1}{2} \cdot 2 (x^{2} + 1)^{\frac{1}{2}} : 11 x^{2} + 1

= 11 x^{2} + 1

Add a constant to the solution

= 11 x^{2} + 1 + C

\frac{t ^{2} + 1}{t ^{2} - 1}

w \to 0 lim (\frac{e ^{2 w} - ( 1 + w )}{w ^{2}})

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

\int \frac{2 x + 3}{x ^{2} + 3 x - 5} d x

What is the integral of (11x)/(sqrt(x^2+1)) ?
The integral of (11x)/(sqrt(x^2+1)) is 11sqrt(x^2+1)+C