What is e^ x x dx equal to ?
We can see that using formula we get (sin x - x cos x) + C. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get (sin x - x cos x) + C.
Ref: NCERT Mathematics Class XII — Integrals
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Solve the initial value problem, dy = ex + ²y dx , y (0) = 0.
Here's the idea in simple terms: after simplifying, y = 1/2 ( 13- 2 e^x ) is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Differential Equations
Evaluate: dxe^x - 1
The logic is straightforward: after simplifying, | e^x - 1e^x | + C is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Integrals
