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Popular >

integral of 1/(xsin(y))

Solution

\int \frac{1}{x sin ( y )} d x

Solution

csc (y) ln ∣ x ∣ + C

Solution steps

\int \frac{1}{x sin ( y )} d x

Take the constant out:

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

= \frac{1}{sin ( y )} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{sin ( y )} ln ∣ x ∣

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= csc (y) ln ∣ x ∣

Add a constant to the solution

= csc (y) ln ∣ x ∣ + C

Popular Examples

derivative of e^{sin(cos(x^n)})

\frac{d}{d x} (e^{s i n (c o s (x^{n}))})

integral of (6x^2)(2x^3+5)^6

\int (6 x^{2}) (2 x^{3} + 5)^{6} d x

integral of (2x+7)/(x^2+3x+3)

\int \frac{2 x + 7}{x ^{2} + 3 x + 3} d x

(dy)/(dx)=((2x(y-1)))/(x^2+3),y(1)=9

\frac{d y}{d x} = \frac{( 2 x ( y - 1 ) )}{x ^{2} + 3}, y (1) = 9

((x^2)/((x-2)^2))^'

(\frac{x ^{2}}{( x - 2 ) ^{2}})^{^{'}}

Frequently Asked Questions (FAQ)

What is the integral of 1/(xsin(y)) ?
The integral of 1/(xsin(y)) is csc(y)ln|x|+C