What is the integral of 5/(sqrt(4-(2x)^2)) ?

The integral of 5/(sqrt(4-(2x)^2)) is 5/2 arcsin(x)+C

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integral of 5/(sqrt(4-(2x)^2))

\int \frac{5}{4 - ( 2 x ) ^{2}} d x

\frac{5}{2} arcsin (x) + C

Solution steps

\int \frac{5}{4 - ( 2 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}{4 - ( 2 x ) ^{2}} d x

4 - (2 x)^{2} = 2 1 - x^{2}

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{1 - x ^{2}} d x = arcsin (x)

= 5 \cdot \frac{1}{2} arcsin (x)

Simplify

5 \cdot \frac{1}{2} arcsin (x) : \frac{5}{2} arcsin (x)

= \frac{5}{2} arcsin (x)

Add a constant to the solution

= \frac{5}{2} arcsin (x) + C

\int_{2}^{3} \frac{1}{x - 3} d x

y = 3 x^{2} - 4

\int 1 + cos (4 x) d x

5 x^{3} + 4 x

\int_{0}^{\infty} \frac{1}{x ^{2} + x} d x

What is the integral of 5/(sqrt(4-(2x)^2)) ?
The integral of 5/(sqrt(4-(2x)^2)) is 5/2 arcsin(x)+C