∫( 2x 3 ) #160; sin #160; xdx ⇒∫ 2xsin #160; x .dx ∫ 3sin #160; x.dx #160; ⇒[ 2x ] ∫sin #160; dx ∫[ 2 dx dx ∫sin #160; xdx ...

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Parametric Differentiation

Find ∫ 2x-3...

Question

Find $\int (2 x - 3) sin x . d x$

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Solution

$\int (2 x - 3) sin x d x \Rightarrow \int 2 x sin x . d x - \int 3 sin x . d x \Rightarrow [2 x] \int sin d x - \int [2 \frac{d x}{d x} \int sin x d x] d x - 3 \int sin x d x \Rightarrow - 2 x cos x + 2 \int cos x d x + 3 cos x \Rightarrow - 2 x cos x + 2 sin x + 3 cos x + c \Rightarrow - 2 x cos x + 3 cos x + 2 sin x + c A n s .$

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