What is the integral of ((2x))/((sqrt(9-x^4))) ?

The integral of ((2x))/((sqrt(9-x^4))) is arcsin(1/3 x^2)+C

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integral of ((2x))/((sqrt(9-x^4)))

\int \frac{( 2 x )}{( 9 - x ^{4} )} d x

arcsin (\frac{1}{3} x^{2}) + C

Solution steps

\int \frac{2 x}{9 - x ^{4}} d x

Take the constant out:

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

= 2 \cdot \int \frac{x}{9 - x ^{4}} d x

Apply u-substitution

= 2 \cdot \int \frac{1}{2 9 - u ^{2}} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int \frac{1}{9 - u ^{2}} d u

Apply Trigonometric Substitution

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

Integral of a constant:

\int a d x = a x

= 2 \cdot \frac{1}{2} \cdot 1 \cdot v

Substitute back

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

Simplify

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

= arcsin (\frac{1}{3} x^{2})

Add a constant to the solution

= arcsin (\frac{1}{3} x^{2}) + C

ln (5 - 2 x)

x \to \infty + lim (x^{12})

\frac{d}{d t} (sin (\frac{t}{2}))

y^{^{'}} = 5

\int e^{\frac{3}{2} x} d x

What is the integral of ((2x))/((sqrt(9-x^4))) ?
The integral of ((2x))/((sqrt(9-x^4))) is arcsin(1/3 x^2)+C