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
#indefinite integral
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x^2+2x+5 dx is equal to:
We can see that we verify 1/2( x + 1 ) x^2 + 2x + 5 + 2 | x + 1 + x^2 + 2x + 5 | + C by full calculation: use standard identity, substitute, simplify step
Ref: NCERT Mathematics Class XII — Integrals
Find the antiderivative of f(x) = 12x³ – 15x² + 64
Recall the rule ∫xⁿdx=x^{n+1}/(n+1). So ∫(12x³-15x²+64)dx=3x⁴-5x³+64x+C. Complete term by term integration.
Ref: NCERT Mathematics Class XII — Integrals
Find the value of b if dx 9-x^2=sin^-1x/b+C
We can see that complete solution: write formula, plug data, do arithmetic. Final value matches 3. Simple and accurate.
Ref: NCERT Mathematics Class XII — Integrals
