What is the integral of 6arcsin(5x) ?

The integral of 6arcsin(5x) is 6(xarcsin(5x)+1/5 sqrt(1-25x^2))+C

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integral of 6arcsin(5x)

\int 6 arcsin (5 x) d x

6 (x arcsin (5 x) + \frac{1}{5} 1 - 25 x^{2}) + C

Solution steps

\int 6 arcsin (5 x) d x

Take the constant out:

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

= 6 \cdot \int arcsin (5 x) d x

Apply Integration By Parts

= 6 (x arcsin (5 x) - \int \frac{5 x}{1 - 25 x ^{2}} d x)

\int \frac{5 x}{1 - 25 x ^{2}} d x = - \frac{1}{5} 1 - 25 x^{2}

= 6 (x arcsin (5 x) - (- \frac{1}{5} 1 - 25 x^{2}))

Simplify

= 6 (x arcsin (5 x) + \frac{1}{5} 1 - 25 x^{2})

Add a constant to the solution

= 6 (x arcsin (5 x) + \frac{1}{5} 1 - 25 x^{2}) + C

What is the integral of 6arcsin(5x) ?
The integral of 6arcsin(5x) is 6(xarcsin(5x)+1/5 sqrt(1-25x^2))+C