What is the integral of 1/((5+x)^2) ?

The integral of 1/((5+x)^2) is -1/(5+x)+C

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integral of 1/((5+x)^2)

\int \frac{1}{( 5 + x ) ^{2}} d x

- \frac{1}{5 + x} + C

Solution steps

\int \frac{1}{( 5 + x ) ^{2}} d x

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = 5 + x

= - \frac{1}{5 + x}

Add a constant to the solution

= - \frac{1}{5 + x} + C

\frac{d}{d x} (\frac{x ^{2}}{( x - 1 )})

\int x^{2} + 6 e^{x} + C d x

\int e x d x

\int \frac{sin ( 2 x )}{1 - sin ^{2} ( x )} d x

y^{^{''}} - y = \frac{e ^{x}}{e ^{x}}