What is the integral of 5/(sqrt(25-x^2)) ?

The integral of 5/(sqrt(25-x^2)) is 5arcsin(1/5 x)+C

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integral of 5/(sqrt(25-x^2))

\int \frac{5}{25 - x ^{2}} d x

5 arcsin (\frac{1}{5} x) + C

Solution steps

\int \frac{5}{25 - x ^{2}} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{25 - x ^{2}} d x

Apply Trigonometric Substitution

: \int 1 d u

= 5 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 5 \cdot 1 \cdot u

Substitute back

u = arcsin (\frac{1}{5} x)

= 5 \cdot 1 \cdot arcsin (\frac{1}{5} x)

Simplify

= 5 arcsin (\frac{1}{5} x)

Add a constant to the solution

= 5 arcsin (\frac{1}{5} x) + C

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

\frac{x}{7} - \frac{7}{x}

\frac{2 s + 12}{s ^{2} + 2 s + 5}

(5 x^{2} + 3)^{\frac{1}{4}}

\int \frac{5 x ^{4} + 5 x ^{3} + 2 x + 1}{x ^{2} + x} d x

What is the integral of 5/(sqrt(25-x^2)) ?
The integral of 5/(sqrt(25-x^2)) is 5arcsin(1/5 x)+C