What is the integral of [((x^2+10x+25))/((x+5))] ?

The integral of [((x^2+10x+25))/((x+5))] is ((x+5)^2)/2+C

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integral of [((x^2+10x+25))/((x+5))]

\int [\frac{( x ^{2} + 10 x + 25 )}{( x + 5 )}] d x

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

Solution steps

\int \frac{x ^{2} + 10 x + 25}{x + 5} d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = x + 5

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

Add a constant to the solution

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

\int \frac{e ^{x}}{1 + 81 e ^{2 x}} d x

f (x) = 1 + sin (x)

\frac{d y}{d x} = \frac{x ^{2} + y ^{2}}{x y}

9 x^{2}

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

What is the integral of [((x^2+10x+25))/((x+5))] ?
The integral of [((x^2+10x+25))/((x+5))] is ((x+5)^2)/2+C