What is the integral of 2cos(x)sin(x)+1/(2x) ?

The integral of 2cos(x)sin(x)+1/(2x) is sin^2(x)+1/2 ln|x|+C

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integral of 2cos(x)sin(x)+1/(2x)

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

sin^{2} (x) + \frac{1}{2} ln ∣ x ∣ + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

= sin^{2} (x) + \frac{1}{2} ln ∣ x ∣

Add a constant to the solution

= sin^{2} (x) + \frac{1}{2} ln ∣ x ∣ + C

\int 17 sin^{2} (x) cos^{2} (x) d x

y^{^{'}} - \frac{7}{x} y = \frac{y ^{3}}{x ^{10}}

75 - 3 x^{2}, [0, 7]

n = 1 \sum \infty n (\frac{7}{8})^{n}

x^{2} + 4 x + 5

What is the integral of 2cos(x)sin(x)+1/(2x) ?
The integral of 2cos(x)sin(x)+1/(2x) is sin^2(x)+1/2 ln|x|+C