What is the integral of (tan(x))/(sin(2x)) ?

The integral of (tan(x))/(sin(2x)) is 1/2 tan(x)+C

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integral of (tan(x))/(sin(2x))

\int \frac{tan ( x )}{sin ( 2 x )} d x

\frac{1}{2} tan (x) + C

Solution steps

\int \frac{tan ( x )}{sin ( 2 x )} d x

Rewrite using trig identities

= \int \frac{tan ( x )}{2 cos ( x ) sin ( x )} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{tan ( x )}{cos ( x ) sin ( x )} d x

Simplify

\frac{tan ( x )}{cos ( x ) sin ( x )} : sec^{2} (x)

= \frac{1}{2} \cdot \int sec^{2} (x) d x

Use the common integral:

\int sec^{2} (x) d x = tan (x)

= \frac{1}{2} tan (x)

Add a constant to the solution

= \frac{1}{2} tan (x) + C

\int \frac{- x}{x + 1 - x + 1} d x

9 π r^{2}

\int \frac{6 x - 1}{x ^{3} ( 2 x - 1 )} d x

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

y = 18 x

What is the integral of (tan(x))/(sin(2x)) ?
The integral of (tan(x))/(sin(2x)) is 1/2 tan(x)+C