# Integrate $$3x^2 (cos⁡x^3+8)$$.

Category: QuestionsIntegrate $$3x^2 (cos⁡x^3+8)$$.
Editor">Editor Staff asked 11 months ago

Integrate $$3x^2 (cos⁡x^3+8)$$.

(a) $$sin⁡x^3-8x^3+C$$

(b) $$sin⁡x^3+8x^3+C$$

(c) –$$sin⁡x^3+8x^3+C$$

(d) $$sin⁡x^3-x^3+C$$

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Editor">Editor Staff answered 11 months ago

The correct answer is (b) $$sin⁡x^3+8x^3+C$$

Easy explanation: By using the method of integration by substitution,

Let x^3=t

Differentiating w.r.t x, we get

3x^2 dx=dt

$$\int 3x^2 \,(cos⁡x^3+8) \,dx=\int (cos⁡t+8)dt$$

$$\int (cos⁡t+8) dt=sin⁡t+8t$$

Replacing t with x^3,we get

$$\int 3x^2 (cos⁡x^3+8) dx=sin⁡x^3+8x^3+C$$