What is the integral of 5/(sqrt(3-3x^2)) ?

The integral of 5/(sqrt(3-3x^2)) is 5(x/(sqrt(3-3x^2))-1/(sqrt(3))(-arcsin(x)+x/(sqrt(1-x^2))))+C

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integral of 5/(sqrt(3-3x^2))

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

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

Solution steps

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

Take the constant out:

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

= 5 \cdot \int \frac{1}{3 - 3 x ^{2}} d x

Apply Integration By Parts

: \frac{x}{3 - 3 x ^{2}} - \int \frac{3 x ^{2}}{( 3 - 3 x ^{2} ) ^{\frac{3}{2}}} d x

= 5 (\frac{x}{3 - 3 x ^{2}} - \int \frac{3 x ^{2}}{( 3 - 3 x ^{2} ) ^{\frac{3}{2}}} d x)

\int \frac{3 x ^{2}}{( 3 - 3 x ^{2} ) ^{\frac{3}{2}}} d x = \frac{1}{3} (- arcsin (x) + \frac{x}{1 - x ^{2}})

= 5 (\frac{x}{3 - 3 x ^{2}} - \frac{1}{3} (- arcsin (x) + \frac{x}{1 - x ^{2}}))

Add a constant to the solution

= 5 (\frac{x}{3 - 3 x ^{2}} - \frac{1}{3} (- arcsin (x) + \frac{x}{1 - x ^{2}})) + C

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What is the integral of 5/(sqrt(3-3x^2)) ?
The integral of 5/(sqrt(3-3x^2)) is 5(x/(sqrt(3-3x^2))-1/(sqrt(3))(-arcsin(x)+x/(sqrt(1-x^2))))+C