What is the integral of (4+3)/(sqrt(1-x^2)) ?

The integral of (4+3)/(sqrt(1-x^2)) is 7arcsin(x)+C

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integral of (4+3)/(sqrt(1-x^2))

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

7 arcsin (x) + C

Solution steps

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

Take the constant out:

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

= (4 + 3) \cdot \int \frac{1}{1 - x ^{2}} d x

Simplify

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

Use the common integral:

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

= 7 arcsin (x)

Add a constant to the solution

= 7 arcsin (x) + C

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What is the integral of (4+3)/(sqrt(1-x^2)) ?
The integral of (4+3)/(sqrt(1-x^2)) is 7arcsin(x)+C