What is the integral of 2sin(x) ?

The integral of 2sin(x) is -2cos(x)+C

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integral of 2sin(x)

\int 2 sin (x) d x

- 2 cos (x) + C

Solution steps

\int 2 sin (x) d x

Take the constant out:

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

= 2 \cdot \int sin (x) d x

Use the common integral:

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

= 2 (- cos (x))

Simplify

= - 2 cos (x)

Add a constant to the solution

= - 2 cos (x) + C

\int \frac{e ^{5 x}}{1 + e ^{5 x}} d x

\int (x^{2} y^{2}) d x

x^{2} - 5 x + \frac{1}{x ^{\frac{3}{2}}}

x \to 3 lim (\frac{x - 3}{1 + x})

\frac{d}{d x} (\frac{( x ^{2} + 1 )}{( x ^{2} - 1 )})