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Popular >

integral of 1/((1-y^2)^{1/2)}

Solution

\int \frac{1}{( 1 - y ^{2} ) ^{\frac{1}{2}}} d y

Solution

arcsin (y) + C

Solution steps

\int \frac{1}{( 1 - y ^{2} ) ^{\frac{1}{2}}} d y

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{( 1 - y ^{2} ) ^{\frac{1}{2}}} = (1 - y^{2})^{- \frac{1}{2}}

= \int (1 - y^{2})^{- \frac{1}{2}} d y

Apply Trigonometric Substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = arcsin (y)

= 1 \cdot arcsin (y)

Simplify

= arcsin (y)

Add a constant to the solution

= arcsin (y) + C

Popular Examples

integral of (x+1)/(x^2+2x+2)

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

integral of (x^2-4)/(x^3-2x^2+x)

\int \frac{x ^{2} - 4}{x ^{3} - 2 x ^{2} + x} d x

derivative of 2^{xsin(x})

\frac{d}{d x} (2^{x s i n (x)})

f (x) = 5 tan (x)

derivative of ecos(x)

\frac{d}{d x} (e cos (x))

Frequently Asked Questions (FAQ)

What is the integral of 1/((1-y^2)^{1/2)} ?
The integral of 1/((1-y^2)^{1/2)} is arcsin(y)+C