What is the integral of 1/(sqrt(28-x^2)) ?

The integral of 1/(sqrt(28-x^2)) is arcsin(1/(2sqrt(7))x)+C

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integral of 1/(sqrt(28-x^2))

\int \frac{1}{28 - x ^{2}} d x

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

Solution steps

\int \frac{1}{28 - 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}{2 7} x)

= 1 \cdot arcsin (\frac{1}{2 7} x)

Simplify

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

Add a constant to the solution

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

\int \frac{3 x}{x - 4} d x

\int (\frac{1 + e ^{2 x}}{4 e ^{x}}) d x

\int \frac{x}{( x + 4 ) ( x - 3 )} d x

\int \frac{1 - x ^{3}}{x ^{2} x} d x

\int x 29 x - 7 d x

What is the integral of 1/(sqrt(28-x^2)) ?
The integral of 1/(sqrt(28-x^2)) is arcsin(1/(2sqrt(7))x)+C