What is the integral of cos(x)x ?

The integral of cos(x)x is xsin(x)+cos(x)+C

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integral of cos(x)x

\int cos (x) x d x

x sin (x) + cos (x) + C

Solution steps

\int cos (x) x d x

Apply Integration By Parts

: x sin (x) - \int sin (x) d x

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

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

= x sin (x) - (- cos (x))

Simplify

= x sin (x) + cos (x)

Add a constant to the solution

= x sin (x) + cos (x) + C

f (x) = \frac{1}{3 x}

f (x) = 2 x^{3} - 4 x - 8 x + 6

n = 0 \sum \infty \frac{1}{e ^{n^{2}}}

\int_{0}^{4} e^{x} sin (x) d x

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