Question

Integration of y cosx dx

Answer 1

Step-by-step explanation:

$\int \sf x \: cosx \: dx \\ \\ \implies x \: \int cos \sf \: x \: dx - \int \{ \frac{d}{dx}(x)\int \: cosx \: dx \}dx \\ \\ \implies \: x \: sinx - \int \: sinx \: dx \\ \\ \boxed{ \implies \: x \: sinx + cosx + c}$

Answer 2

$\mathfrak{\bf{\underline{\underline{Qᴜᴇsᴛɪᴏɴ \ :}}}}$

$\impliesㅤㅤㅤㅤㅤ\int \: x \: \: cosx \: dx$

$\mathfrak{\bf{\underline{\underline{Sᴏʟᴜᴛɪᴏɴ \ :}}}}$

$\impliesㅤㅤ \: \int \: x \: cosx \: dx \: \\ \implies \: x\int \: \cos x \: dx \: - \int \: {{( \frac{d}{dx} (x) \: \int \: cos \: x \:)}} \\ \implies \: x \: sin x \: - \: \int \: sinx \: dx \: \\ \implies \: \underline{\boxed{ \blue{\boxed {x \: sinx \: + \: cosx + c}}}}$