What is the integral of-2/(sqrt(81-49x^2)) ?

The integral of-2/(sqrt(81-49x^2)) is -2/7 arcsin(7/9 x)+C

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integral of-2/(sqrt(81-49x^2))

\int - \frac{2}{81 - 49 x ^{2}} d x

- \frac{2}{7} arcsin (\frac{7}{9} x) + C

Solution steps

\int - \frac{2}{81 - 49 x ^{2}} d x

Take the constant out:

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

= - 2 \cdot \int \frac{1}{81 - 49 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{7} d u

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

Take the constant out:

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

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

Integral of a constant:

\int a d x = a x

= - 2 \cdot \frac{1}{7} \cdot 1 \cdot u

Substitute back

u = arcsin (\frac{7}{9} x)

= - 2 \cdot \frac{1}{7} \cdot 1 \cdot arcsin (\frac{7}{9} x)

Simplify

- 2 \cdot \frac{1}{7} \cdot 1 \cdot arcsin (\frac{7}{9} x) : - \frac{2}{7} arcsin (\frac{7}{9} x)

= - \frac{2}{7} arcsin (\frac{7}{9} x)

Add a constant to the solution

= - \frac{2}{7} arcsin (\frac{7}{9} x) + C

\int \frac{3 x ^{2}}{( 49 + x ^{2} ) ^{2}} d x

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\int 0.024 \cdot (0.03 q^{2} - 2 q) + 130 d q

\int \frac{x - 2}{x ^{2} - 6 x} d x

What is the integral of-2/(sqrt(81-49x^2)) ?
The integral of-2/(sqrt(81-49x^2)) is -2/7 arcsin(7/9 x)+C