What is the integral of+x/(sqrt(3-x^4)) ?

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

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integral of+x/(sqrt(3-x^4))

\int + \frac{x}{3 - x ^{4}} d x

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

Solution steps

\int \frac{x}{3 - x ^{4}} d x

Apply u-substitution

: \int \frac{1}{2 3 - u ^{2}} d u

= \int \frac{1}{2 3 - u ^{2}} 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}{3 - u ^{2}} d u

Apply Trigonometric Substitution

: \int 1 d v

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

Integral of a constant:

\int a d x = a x

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

Substitute back

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

Simplify

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

Add a constant to the solution

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

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 1

\frac{\partial}{\partial x} (x^{2} + x y^{2} + y^{2})

\int_{0}^{1} (x^{2} + 8) (e^{- x}) d x

x \to 2 - lim (\frac{x - 3}{x - 2})

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

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