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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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:

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

Add a constant to the solution

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

(4 + sec (θ)) sin (θ)

e^{x^{4} + 3 x}

\int_{1}^{5} \frac{6}{x} d x

\int 6 x + 8 d x

\frac{d}{d x} (\frac{( e ^{x} - e ^{- 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