What is the integral of arcsin(7x) ?

The integral of arcsin(7x) is xarcsin(7x)+1/7 sqrt(1-49x^2)+C

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integral of arcsin(7x)

\int arcsin (7 x) d x

x arcsin (7 x) + \frac{1}{7} 1 - 49 x^{2} + C

Solution steps

\int arcsin (7 x) d x

Apply Integration By Parts

: x arcsin (7 x) - \int \frac{7 x}{1 - 49 x ^{2}} d x

= x arcsin (7 x) - \int \frac{7 x}{1 - 49 x ^{2}} d x

\int \frac{7 x}{1 - 49 x ^{2}} d x = - \frac{1}{7} 1 - 49 x^{2}

= x arcsin (7 x) - (- \frac{1}{7} 1 - 49 x^{2})

Simplify

= x arcsin (7 x) + \frac{1}{7} 1 - 49 x^{2}

Add a constant to the solution

= x arcsin (7 x) + \frac{1}{7} 1 - 49 x^{2} + C

\frac{d}{d x} (arctan (\frac{π}{x}))

\frac{1}{tan ( x )}

\frac{\partial}{\partial y} (5 + x ln (x y - 7))

x^{2} + \frac{1}{x ^{2}}

\frac{d}{d x} ((x + 3) ln (4 x + 2))

What is the integral of arcsin(7x) ?
The integral of arcsin(7x) is xarcsin(7x)+1/7 sqrt(1-49x^2)+C