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

The integral of (1+4x)/(sqrt(1+x+2x^2)) is 2sqrt(1+x+2x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

2 1 + x + 2 x^{2} + C

Solution steps

\int \frac{1 + 4 x}{1 + x + 2 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 = 1 + x + 2 x^{2}

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

Apply radical rule:

= 2 1 + x + 2 x^{2}

Add a constant to the solution

= 2 1 + x + 2 x^{2} + C

\frac{d}{d x} (\frac{2 x ^{2} - 4 x + 3}{2 - 3 x})

\int f (r) d r

\int \frac{t}{t ^{4} + 6} d t

\int \frac{x ^{4}}{3 - x ^{5}} d x

\frac{d}{d x} (\frac{a x + b}{a x - b})

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