If 19-16x^2dx= ^-1 ( x)+c then + 1=
In easy words, we verify 1 by full calculation: use standard identity, substitute, simplify step by step to reach 1.
Ref: NCERT Mathematics Class XII — Integrals
#antiderivative
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Evaluate e^x( 1/x - 1x^2 )dx
From the definition, complete solution: write formula, plug data, do arithmetic. Final value matches e^xx + c. Simple and accurate.
Ref: NCERT Mathematics Class XII — Integrals
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
