What is the integral of 1/(sqrt(7-x^2)) ?

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

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integral of 1/(sqrt(7-x^2))

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

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

Solution steps

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

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

Simplify

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

Add a constant to the solution

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

\int_{0}^{2} \frac{x - 2}{x - 1} d x

\int \frac{x ^{2}}{8 - x} d x

(x^{2} + 15)^{2}

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

\frac{d}{d x} (\frac{1}{4} cos^{4} (x^{3}) - sin^{2} (6 x))

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