What is the integral of 5/(sqrt(1-9x^2))+7x ?

The integral of 5/(sqrt(1-9x^2))+7x is 5/3 arcsin(3x)+(7x^2)/2+C

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integral of 5/(sqrt(1-9x^2))+7x

\int \frac{5}{1 - 9 x ^{2}} + 7 x d x

\frac{5}{3} arcsin (3 x) + \frac{7 x ^{2}}{2} + C

Solution steps

\int \frac{5}{1 - 9 x ^{2}} + 7 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{5}{1 - 9 x ^{2}} d x + \int 7 x d x

\int \frac{5}{1 - 9 x ^{2}} d x = \frac{5}{3} arcsin (3 x)

\int 7 x d x = \frac{7 x ^{2}}{2}

= \frac{5}{3} arcsin (3 x) + \frac{7 x ^{2}}{2}

Add a constant to the solution

= \frac{5}{3} arcsin (3 x) + \frac{7 x ^{2}}{2} + C

\frac{\partial}{\partial x} (y^{2} - 2 x y)

\frac{d}{d x} (\frac{x}{2})

f (x) = \frac{5}{x}, at x = 4, x = 5

y = (9 x^{2} - 18 x + 18) e^{- 4 x}

\int x^{2} e^{3 x} d x

What is the integral of 5/(sqrt(1-9x^2))+7x ?
The integral of 5/(sqrt(1-9x^2))+7x is 5/3 arcsin(3x)+(7x^2)/2+C