Question

integral (2x²+e^x)dc
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Answer 1

EXPLANATION.

Integral of = ∫ ( 2x² + eˣ)dx.

Using the formula we get,

( a ) = eˣdx = eˣ + c.

(b) = xⁿdx = xⁿ⁺¹/n + 1 + c.

⇒ ∫(2x²)dx + ∫(eˣ)dx.

⇒ 2x²⁺¹/2 + 1 + eˣ + c.

⇒ 2x³/3 + eˣ + c.

                           

MORE INFORMATION.

(1) = ∫sin xdx = -cosx + c.

(2) = ∫cos xdx = sinx + c.

(3) = ∫tan xdx = -㏒|cos x| + c  or ㏒|sec x | + c.

(4) = ∫cot xdx = ㏒| sin x | + c  or  ㏒| cosec x | + c.

(5) = ∫sec xdx = ㏒| sec x + tan x | + c or ㏒ | tan ( π/4 + x/2 ) | + c.

(6) = ∫cosec xdx = ㏒| cosec x - cot x | + c or ㏒ | tan x/2 | + c.

(7) = ∫aˣdx = aˣ/㏑a + c.