What is the integral of 1/((4x+5)^{10)} ?

The integral of 1/((4x+5)^{10)} is -1/(36(4x+5)^9)+C

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integral of 1/((4x+5)^{10)}

\int \frac{1}{( 4 x + 5 ) ^{10}} d x

- \frac{1}{36 ( 4 x + 5 ) ^{9}} + C

Solution steps

\int \frac{1}{( 4 x + 5 ) ^{10}} d x

Apply u-substitution

: \int \frac{1}{4 u ^{10}} d u

= \int \frac{1}{4 u ^{10}} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{1}{u ^{10}} d u

Apply the Power Rule

: - \frac{1}{9 u ^{9}}

= \frac{1}{4} (- \frac{1}{9 u ^{9}})

Substitute back

u = 4 x + 5

= \frac{1}{4} (- \frac{1}{9 ( 4 x + 5 ) ^{9}})

Simplify

\frac{1}{4} (- \frac{1}{9 ( 4 x + 5 ) ^{9}}) : - \frac{1}{36 ( 4 x + 5 ) ^{9}}

= - \frac{1}{36 ( 4 x + 5 ) ^{9}}

Add a constant to the solution

= - \frac{1}{36 ( 4 x + 5 ) ^{9}} + C

y^{^{''}} + 2 y^{^{'}} + 10 y = 0

f (x) = arcsin (5 x)

x \to 5 lim (\frac{x - 5}{2 x - 10})

x \to - 1 lim (\frac{x ^{2} - 9}{x + 1})

n = 2 \sum \infty \frac{2}{n ^{2} + 1}

What is the integral of 1/((4x+5)^{10)} ?
The integral of 1/((4x+5)^{10)} is -1/(36(4x+5)^9)+C