What is the integral of (35)/(1-cos(5x)) ?

The integral of (35)/(1-cos(5x)) is -7cot((5x)/2)+C

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integral of (35)/(1-cos(5x))

\int \frac{35}{1 - cos ( 5 x )} d x

- 7 cot (\frac{5 x}{2}) + C

Solution steps

\int \frac{35}{1 - cos ( 5 x )} d x

Take the constant out:

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

= 35 \cdot \int \frac{1}{1 - cos ( 5 x )} d x

Apply u-substitution

= 35 \cdot \int \frac{1}{5 ( 1 - cos ( u ) )} d u

Take the constant out:

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

= 35 \cdot \frac{1}{5} \cdot \int \frac{1}{1 - cos ( u )} d u

Apply u-substitution

= 35 \cdot \frac{1}{5} \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

= 35 \cdot \frac{1}{5} (- \frac{1}{v})

Substitute back

= 35 \cdot \frac{1}{5} (- \frac{1}{tan ( \frac{5 x}{2} )})

Simplify

35 \cdot \frac{1}{5} (- \frac{1}{tan ( \frac{5 x}{2} )}) : - 7 cot (\frac{5 x}{2})

= - 7 cot (\frac{5 x}{2})

Add a constant to the solution

= - 7 cot (\frac{5 x}{2}) + C

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

\frac{d}{d x} (\frac{( ( 0.06 x ^{2} ) + 17 x + 340 )}{x})

l a pl a ce t r an s f or m 2 e^{\frac{t}{2}}

\int_{2}^{t} \frac{1}{( 5 x ^{5} )} d x

\int \frac{1}{P - P ^{2}} d P

What is the integral of (35)/(1-cos(5x)) ?
The integral of (35)/(1-cos(5x)) is -7cot((5x)/2)+C