What is the integral of 1/((3x+1)^2) ?

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

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integral of 1/((3x+1)^2)

\int \frac{1}{( 3 x + 1 ) ^{2}} d x

- \frac{1}{3 ( 3 x + 1 )} + C

Solution steps

\int \frac{1}{( 3 x + 1 ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{3 u ^{2}} d u

= \int \frac{1}{3 u ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= \frac{1}{3} (- \frac{1}{u})

Substitute back

u = 3 x + 1

= \frac{1}{3} (- \frac{1}{3 x + 1})

Simplify

\frac{1}{3} (- \frac{1}{3 x + 1}) : - \frac{1}{3 ( 3 x + 1 )}

= - \frac{1}{3 ( 3 x + 1 )}

Add a constant to the solution

= - \frac{1}{3 ( 3 x + 1 )} + C

e^{(x - 1)^{2}}

\int_{0}^{\infty} t^{2} d t

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

\frac{1}{4 x - 3}

\int_{0}^{1} 5 e^{- 3 x} d x

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