Question

solve integrals plzz help me.​

Answer 1

Answer

∫ x cos x dx = x sin x + cos x + c

Given

$\bullet \;\; \rm \int x\ cos\ x\ dx$

To Find

Integral value

Concept Used

We need to use ILATE rule .

I denotes Inverse function

L denotes Logarithmic function

A denotes Algebraic function

T denotes Trigonometric function

E denotes Exponential function

I > L > A > T > E [ Preference ]

Solution

$\rm \int x\ cos\ x\ dx$

$\boxed{\begin{minipage}{4cm} \rm Let,u=x\ \;\; dv=cos\ x\ dx\\\\\rightarrow du=dx\ \;\; v=sin\ x \end{minipage}}$

$\implies \rm uv-\int v\ du\\\\\implies \rm x\ sin\ x - \int sin\ x\ dx\\\\\implies \rm x\ sin\ x - (-cos\ x)\\\\\implies \rm x\ sin\ x+cosx+c$

$\bf \int x\ cos\ x\ dx=x\ sin\ x+cos\ x +c$