What is the integral of 1/((v+7)^3) ?

The integral of 1/((v+7)^3) is -1/(2(v+7)^2)+C

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integral of 1/((v+7)^3)

\int \frac{1}{( v + 7 ) ^{3}} d v

- \frac{1}{2 ( v + 7 ) ^{2}} + C

Solution steps

\int \frac{1}{( v + 7 ) ^{3}} d v

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= - \frac{1}{2 u ^{2}}

Substitute back

u = v + 7

= - \frac{1}{2 ( v + 7 ) ^{2}}

Add a constant to the solution

= - \frac{1}{2 ( v + 7 ) ^{2}} + C

f (x) = x^{2 π}

\int \frac{x - 2}{x} d x

\frac{s}{( s - 2 ) ^{2}}

\int \frac{e ^{- b x}}{1 - e ^{- b x}} d x

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

What is the integral of 1/((v+7)^3) ?
The integral of 1/((v+7)^3) is -1/(2(v+7)^2)+C