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Popular >

integral of sin(yx)

Solution

\int sin (y x) d x

Solution

- \frac{1}{y} cos (y x) + C

Solution steps

\int sin (y x) d x

Apply u-substitution

: \int \frac{sin ( u )}{y} d u

= \int \frac{sin ( u )}{y} d u

Take the constant out:

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

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

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{y} (- cos (u))

Substitute back

u = y x

= \frac{1}{y} (- cos (y x))

Simplify

= - \frac{1}{y} cos (y x)

Add a constant to the solution

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

Popular Examples

integral of (x^3+1)/(x^3-8)

\int \frac{x ^{3} + 1}{x ^{3} - 8} d x

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

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

integral of (3x-x^2)

\int (3 x - x^{2}) d x

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

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

integral of ((-6x^6-4x)/(x^2)-4e^{6x})

\int (\frac{- 6 x ^{6} - 4 x}{x ^{2}} - 4 e^{6 x}) d x

Frequently Asked Questions (FAQ)

What is the integral of sin(yx) ?
The integral of sin(yx) is -1/y cos(yx)+C