Question

Find the integral of 2 sin⁡2x+3.

(a) sin⁡2x+3x+C

(b) -cos⁡2x-3x^3+C

(c) -cos⁡2x+3x+C

(d) cos⁡2x-3x+12+C

I got this question by my school teacher while I was bunking the class.

This intriguing question comes from Integration as an Inverse Process of Differentiation topic in portion Integrals of Mathematics – Class 12

Answer 1

Right choice is (c) -cos⁡2x+3x+C

Best explanation: To find ∫ 2 sin⁡2x+3 dx

\(\int \,2 \,sin⁡2x+3 \,dx=\int \,2 \,sin⁡2x \,dx + \int \,3 \,dx\)

\(\int \,2 \,sin⁡2x+3 \,dx=2\int \,sin⁡2x \,dx+3\int \,dx\)

\(\int \,2 \,sin⁡2x+3 \,dx=\frac{-2 cos⁡2x}{2}+3x\)

∴∫2 sin⁡2x+3 dx=-cos⁡2x+3x+C