e^x(2 x+12 x) dx Option 1: 12 x e^x+C Option 2: -e^x x+C Option 3: -12 sqrt(x) e^x+C Option 4: e^x sqrt(x)+C

The answer is 'e^x sqrt(x)+C'. View full solution:

Calculus > Integrals

Medium

core

$\int \mathrm{e}^{\mathrm{x}}\left(\frac{2 \mathrm{x}+1}{2 \sqrt{\mathrm{x}}}\right) \mathrm{dx}$

$\frac{1}{2 \sqrt{\mathrm{x}}} \mathrm{e}^{\mathrm{x}}+\mathrm{C}$

$-\mathrm{e}^{\mathrm{x}} \sqrt{\mathrm{x}}+C$

$-\frac{1}{2 \sqrt{x}} e^{x}+C$

$e^{x} \sqrt{x}+C$

✅ Correct Option: 4

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Match List-I with List-II

List-I	List-II
(A) The value of $\int_{0}^{4} \vert x\vert \, dx$ is	(I) 3
(B) The value of $\int_{-2}^{2} \vert x\vert \, dx$ is	(II) -1
(C) The value of $\int_{0}^{3} [x] \, dx$ is	(III) 8
(D) The value of $\int_{-1}^{1} [x] \, dx$ is	(IV) 4

Choose the correct answer from the options given below: