integrate x^2 cos(x^3) dx
Answers
Answered by
10
EXPLANATION.
⇒ ∫x².cos(x³)dx.
As we know that,
By using the substitution method, we get.
⇒ x³ = t.
Differentiate w.r.t x, we get.
⇒ 3x²dx = dt.
⇒ x²dx = dt/3.
Put the value in the equation, we get.
⇒ ∫cos(t)dt/3.
⇒ 1/3∫cos(t)dt.
⇒ 1/3 sin(t) + c.
Put the value of t = x³ in the equation, we get.
⇒ 1/3 sin(x³) + c.
MORE INFORMATION.
Standard integrals.
(1) = ∫0.dx = c.
(2) = ∫1.dx = x + c.
(3) = ∫k dx = kx + c, (k ∈ R).
(4) = ∫xⁿdx = xⁿ⁺¹/n + 1 + c, (n ≠ -1).
(5) = ∫dx/x = ㏒(x) + c.
(6) = ∫eˣdx = eˣ + c.
(7) = ∫aˣdx = aˣ/㏒(a) + c = aˣ㏒(e) + c.
Similar questions