What is the integral of (3x)/(sqrt(7-x^2)) ?

The integral of (3x)/(sqrt(7-x^2)) is -3sqrt(7-x^2)+C

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integral of (3x)/(sqrt(7-x^2))

\int \frac{3 x}{7 - x ^{2}} d x

- 3 7 - x^{2} + C

Solution steps

\int \frac{3 x}{7 - x ^{2}} d x

Take the constant out:

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

= 3 \cdot \int \frac{x}{7 - x ^{2}} d x

Apply u-substitution

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

= 3 \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

= 3 (- \frac{1}{2} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

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

= 3 (- \frac{1}{2} \cdot 2 u^{\frac{1}{2}})

Substitute back

u = 7 - x^{2}

= 3 (- \frac{1}{2} \cdot 2 (7 - x^{2})^{\frac{1}{2}})

Simplify

3 (- \frac{1}{2} \cdot 2 (7 - x^{2})^{\frac{1}{2}}) : - 3 7 - x^{2}

= - 3 7 - x^{2}

Add a constant to the solution

= - 3 7 - x^{2} + C

\frac{d}{d x} (- \frac{4 x}{( x ^{2} + 4 ) ^{2}})

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x \to 5 lim (4)

x^{8 c o s (x)}

x y^{^{'}} + (1 + 6 x) y = 24 e^{- 6 x}

What is the integral of (3x)/(sqrt(7-x^2)) ?
The integral of (3x)/(sqrt(7-x^2)) is -3sqrt(7-x^2)+C