Find the integral of $$8x^3+1$$.

Category: QuestionsFind the integral of $$8x^3+1$$.
Editor">Editor Staff asked 11 months ago

Find the integral of $$8x^3+1$$.

(a) 2x^4+x+C

(b) 2x^6-5x+C

(c) 2x^4-x+C

(d) 2x^4+x^2 C

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This interesting question is from Integration as an Inverse Process of Differentiation topic in chapter Integrals of Mathematics – Class 12
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Editor">Editor Staff answered 11 months ago

Right option is (a) 2x^4+x+C

Explanation: $$\int \,8x^{3+1} \,dx$$

Using $$\int \,x^n \,dx=\frac{x^{n+1}}{n+1}$$, we get

$$\int \,8x^{3+1} \,dx=\int 8x^3 \,dx+\int \,1 \,dx$$

=$$\frac{8x^{3+1}}{3+1}+x$$

=$$\frac{8x^4}{4}+x$$

=2x^4+x+C.