What is the integral of 1/(sqrt(a^2-u^2)) ?

The integral of 1/(sqrt(a^2-u^2)) is arcsin(u/a)+C

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integral of 1/(sqrt(a^2-u^2))

\int \frac{1}{a ^{2} - u ^{2}} d u

arcsin (\frac{u}{a}) + C

Solution steps

\int \frac{1}{a ^{2} - u ^{2}} d u

Apply Trigonometric Substitution

: \int 1 d v

= \int 1 d v

Integral of a constant:

\int a d x = a x

= 1 \cdot v

Substitute back

v = arcsin (\frac{1}{a} u)

= 1 \cdot arcsin (\frac{1}{a} u)

Simplify

1 \cdot arcsin (\frac{1}{a} u) : arcsin (\frac{u}{a})

= arcsin (\frac{u}{a})

Add a constant to the solution

= arcsin (\frac{u}{a}) + C

\int_{0}^{x} sin (\frac{π t ^{2}}{2}) d t

\frac{\partial}{\partial x} (e^{- x^{2}})

\int (11 x + 5) d x

\int x^{3} 1 + 4 x^{2} d x

\frac{d y}{d x}, y^{6} = x^{5}

What is the integral of 1/(sqrt(a^2-u^2)) ?
The integral of 1/(sqrt(a^2-u^2)) is arcsin(u/a)+C