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

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

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integral of (sin(x))/(sqrt(7-cos^2(x)))

\int \frac{sin ( x )}{7 - cos ^{2} ( x )} d x

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

Solution steps

\int \frac{sin ( x )}{7 - cos ^{2} ( x )} d x

Apply u-substitution

: \int - \frac{1}{7 - u ^{2}} d u

= \int - \frac{1}{7 - u ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{7 - 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

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

Simplify

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

Add a constant to the solution

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

\int \frac{x ^{3} - 11 x - 26}{x ^{2} - 2 x - 8} d x

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

\frac{d}{d y} ((x + y)^{2})

\frac{x ^{2}}{x ^{2} - 1}

x \to 0 lim (\frac{6}{x ^{2}})

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