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Popular >

integral of 4sin(x)cos(x)

Solution

\int 4 sin (x) cos (x) d x

Solution

2 sin^{2} (x) + C

Solution steps

\int 4 sin (x) cos (x) d x

Take the constant out:

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

= 4 \cdot \int sin (x) cos (x) d x

Apply u-substitution

: \int u d u

= 4 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 4 \cdot \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= 4 \cdot \frac{sin ^{2} ( x )}{2}

Simplify

4 \cdot \frac{sin ^{2} ( x )}{2} : 2 sin^{2} (x)

= 2 sin^{2} (x)

Add a constant to the solution

= 2 sin^{2} (x) + C

Popular Examples

limit as x approaches 0 of ((sin^3(2x)))/((sin^3(3x)))

x \to 0 lim (\frac{( sin ^{3} ( 2 x ) )}{( sin ^{3} ( 3 x ) )})

integral of sin(x)(x)

\int sin (x) (x) d x

integral of ((x-2))/((x-1))

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

integral of 22e^x

\int 22 e^{x} d x

integral of (e^{x^2}-1)/x

\int \frac{e ^{x^{2}} - 1}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of 4sin(x)cos(x) ?
The integral of 4sin(x)cos(x) is 2sin^2(x)+C