What is the integral of 1/(sqrt(441-x^2)) ?

The integral of 1/(sqrt(441-x^2)) is arcsin(1/21 x)+C

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integral of 1/(sqrt(441-x^2))

\int \frac{1}{441 - x ^{2}} d x

arcsin (\frac{1}{21} x) + C

Solution steps

\int \frac{1}{441 - x ^{2}} d x

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 (\frac{1}{21} x)

= 1 \cdot arcsin (\frac{1}{21} x)

Simplify

= arcsin (\frac{1}{21} x)

Add a constant to the solution

= arcsin (\frac{1}{21} x) + C

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

\frac{d}{d x} (3 x^{2} - 12 x)

\int ln (12 x) d x

2 x y y^{^{'}} = 4 x^{2} + 3 y^{2}

\int_{0}^{1} \int_{- 1}^{∣ x ∣^{- 1}} (x + y)^{2} d y d x

What is the integral of 1/(sqrt(441-x^2)) ?
The integral of 1/(sqrt(441-x^2)) is arcsin(1/21 x)+C