What is the integral of ((4+10x))/(sqrt(7+4x+5x^2)) ?

The integral of ((4+10x))/(sqrt(7+4x+5x^2)) is 2sqrt(7+4x+5x^2)+C

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integral of ((4+10x))/(sqrt(7+4x+5x^2))

\int \frac{( 4 + 10 x )}{7 + 4 x + 5 x ^{2}} d x

2 7 + 4 x + 5 x^{2} + C

Solution steps

\int \frac{4 + 10 x}{7 + 4 x + 5 x ^{2}} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 2 u^{\frac{1}{2}}

Substitute back

u = 7 + 4 x + 5 x^{2}

= 2 (7 + 4 x + 5 x^{2})^{\frac{1}{2}}

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 7 + 4 x + 5 x^{2}

Add a constant to the solution

= 2 7 + 4 x + 5 x^{2} + C

y^{^{'}} + 3 y = e^{- 2 x}

\int_{- 3}^{4} ((y + 12) - (y^{2})) d y

y^{^{''}} + 7 y^{^{'}} + 6 y = 0

f (x) = 2 (x)^{3} ln (x)

x \to - 2 lim (\frac{x ^{2} + 4}{x + 2})

What is the integral of ((4+10x))/(sqrt(7+4x+5x^2)) ?
The integral of ((4+10x))/(sqrt(7+4x+5x^2)) is 2sqrt(7+4x+5x^2)+C