Question

Find the following integral : $\int (2x^2+e^x) \, dx$

Answer 1

Answer:

Step-by-step explanation:

Concept:

$1.\int[f(x)+g(x)]\:dx=\int{f(x)}\;dx+\int{g(x)}\;dx\\\\2.\int{x^n}\:dx=\frac{x^{n+1}}{n+1}+c\\\\3.\int{e^x}\:dx=e^x+c$

Now,

$\int{[2x^2+e^x]}\:dx\\\\=\int{2x^2}\:dx+\int{e^x}\:dx\\\\=2\int{x^2}\:dx+\int{e^x}\:dx\\\\=2(\frac{x^3}{3})+e^x+c$