What is the integral of (70)/(49-x^2) ?

The integral of (70)/(49-x^2) is 10(1/2 ln| x/7+1|-1/2 ln| x/7-1|)+C

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integral of (70)/(49-x^2)

\int \frac{70}{49 - x ^{2}} d x

10 (\frac{1}{2} ln \frac{x}{7} + 1 - \frac{1}{2} ln \frac{x}{7} - 1) + C

Solution steps

\int \frac{70}{49 - x ^{2}} d x

Take the constant out:

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

= 70 \cdot \int \frac{1}{49 - x ^{2}} d x

Apply Integral Substitution

= 70 \cdot \int \frac{1}{7 ( - u ^{2} + 1 )} d u

Take the constant out:

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

= 70 \cdot \frac{1}{7} \cdot \int \frac{1}{- u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{- u ^{2} + 1} d u = \frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2}

= 70 \cdot \frac{1}{7} (\frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2})

Substitute back

u = \frac{x}{7}

= 70 \cdot \frac{1}{7} (\frac{ln \frac{x}{7} + 1}{2} - \frac{ln \frac{x}{7} - 1}{2})

Simplify

70 \cdot \frac{1}{7} (\frac{ln \frac{x}{7} + 1}{2} - \frac{ln \frac{x}{7} - 1}{2}) : 10 (\frac{1}{2} ln \frac{x}{7} + 1 - \frac{1}{2} ln \frac{x}{7} - 1)

= 10 (\frac{1}{2} ln \frac{x}{7} + 1 - \frac{1}{2} ln \frac{x}{7} - 1)

Add a constant to the solution

= 10 (\frac{1}{2} ln \frac{x}{7} + 1 - \frac{1}{2} ln \frac{x}{7} - 1) + C

f (x) x^{2} + 3 a y, x = - 1

5 x - x^{2}, x

\frac{\partial}{\partial x} (x^{4} y^{5} + 3 x^{9} y)

\int (3 x + 4 y) d x

\frac{d}{d u} (\frac{v}{u - v})

What is the integral of (70)/(49-x^2) ?
The integral of (70)/(49-x^2) is 10(1/2 ln| x/7+1|-1/2 ln| x/7-1|)+C