Find the integral of \int 3e^x+\frac{2}{x}+x^3 dx.

Category: QuestionsFind the integral of \int 3e^x+\frac{2}{x}+x^3 dx.
Editor">Editor Staff asked 11 months ago

Find the integral of \int 3e^x+\frac{2}{x}+x^3 dx
.
 
(a) 3e^3x+\frac{2}{x}-\frac{x^4}{4}+c
 
 
(b) 3e^x+2 \,log⁡x+\frac{x^4}{4}+c
 
 
(c) e^x+2 \,log⁡x+\frac{x^4}{4}+c
 
 
(d) 3e^x-\frac{2}{x^2}+\frac{x^4}{4}+c
 
 
I got this question in a job interview.
 
Question is from Integration as an Inverse Process of Differentiation topic in portion Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

1 Answers
Editor">Editor Staff answered 11 months ago

The correct answer is (b)
3
e
x
+2logx+
x
4
4
+c
 
 
The explanation: To find
∫3
e
x
+
2
x
+
x
3
dx
 
 
∫3
e
x
+
2
x
+
x
3
dx=3∫
e
x
dx+2∫
1
x
dx+∫
x
3
dx
 
 

e
x
dx=
e
x
 
 

1
x
dx=logx
 
 

∫3
e
x
+
2
x
+
x
3
dx=3
e
x
+2logx+
x
4
4
+c