What is the integral of (x^2)/(x+7) ?

The integral of (x^2)/(x+7) is ((x+7)^2)/2-14(x+7)+49ln|x+7|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2)/(x+7)

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

\frac{( x + 7 ) ^{2}}{2} - 14 (x + 7) + 49 ln ∣ x + 7 ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{( u - 7 ) ^{2}}{u} d u

= \int \frac{( u - 7 ) ^{2}}{u} d u

Expand

\frac{( u - 7 ) ^{2}}{u} : u - 14 + \frac{49}{u}

= \int u - 14 + \frac{49}{u} d u

Apply the Sum Rule:

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

= \int u d u - \int 14 d u + \int \frac{49}{u} d u

\int u d u = \frac{u ^{2}}{2}

\int 14 d u = 14 u

\int \frac{49}{u} d u = 49 ln ∣ u ∣

= \frac{u ^{2}}{2} - 14 u + 49 ln ∣ u ∣

Substitute back

u = x + 7

= \frac{( x + 7 ) ^{2}}{2} - 14 (x + 7) + 49 ln ∣ x + 7 ∣

Add a constant to the solution

= \frac{( x + 7 ) ^{2}}{2} - 14 (x + 7) + 49 ln ∣ x + 7 ∣ + C

y^{^{''}} - 2 y^{^{'}} - 15 y = e^{3 x} cos (2 x)

\frac{d}{d x} (2 x - 7)

\int cos^{5} (t) d t

cos (π - 6 x)

y = 2 sin (x) + c e^{- x} cos (x)

What is the integral of (x^2)/(x+7) ?
The integral of (x^2)/(x+7) is ((x+7)^2)/2-14(x+7)+49ln|x+7|+C