What is the integral of (10)/((20x+1)^{23)} ?

The integral of (10)/((20x+1)^{23)} is -1/(44(20x+1)^{22)}+C

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integral of (10)/((20x+1)^{23)}

\int \frac{10}{( 20 x + 1 ) ^{23}} d x

- \frac{1}{44 ( 20 x + 1 ) ^{22}} + C

Solution steps

\int \frac{10}{( 20 x + 1 ) ^{23}} d x

Take the constant out:

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

= 10 \cdot \int \frac{1}{( 20 x + 1 ) ^{23}} d x

Apply u-substitution

: \int \frac{1}{20 u ^{23}} d u

= 10 \cdot \int \frac{1}{20 u ^{23}} d u

Take the constant out:

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

= 10 \cdot \frac{1}{20} \cdot \int \frac{1}{u ^{23}} d u

Apply the Power Rule

: - \frac{1}{22 u ^{22}}

= 10 \cdot \frac{1}{20} (- \frac{1}{22 u ^{22}})

Substitute back

u = 20 x + 1

= 10 \cdot \frac{1}{20} (- \frac{1}{22 ( 20 x + 1 ) ^{22}})

Simplify

10 \cdot \frac{1}{20} (- \frac{1}{22 ( 20 x + 1 ) ^{22}}) : - \frac{1}{44 ( 20 x + 1 ) ^{22}}

= - \frac{1}{44 ( 20 x + 1 ) ^{22}}

Add a constant to the solution

= - \frac{1}{44 ( 20 x + 1 ) ^{22}} + C

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What is the integral of (10)/((20x+1)^{23)} ?
The integral of (10)/((20x+1)^{23)} is -1/(44(20x+1)^{22)}+C