Question

Differentiate.

Answer 1

\[(5x ^{2}+e ^{2x}) dx\]

Answer 2

integral of the function above *

Answer 3

So integrate?

Answer 4

the instructions say differentiate.
there's suppose to be an integral sign infront of my function above.

Answer 5

\[∫ (5x ^{2}+e ^{2x})dx\]

Answer 6

Let's start by factoring out the constants

\[5\int\limits_{?}^{?}x^2dx + \int\limits_{?}^{?}e^2x dx\]

Answer 7

oops, that second part should be e^(2x)

Answer 8

i know i have to split it up so it looks like ∫ 5x^2 dx + ∫ e^2x dx

Answer 9

then i assume i take out the 5.

Answer 10

The integral of e^(2x) is e^(2x) / 2

The integral of x^2 is x^3 / 3

So, we end up with:

\[\frac{ 5x^3 }{ 3 } + \frac{ e^{2x} }{ 2 }\] + C

Understand?

Answer 11

no i dont sorry.

Answer 12

No need to apologize. Which part are you confused with.

Answer 13

when you say the integral of and then you just make it into a fraction.

Answer 14

i wrote it like: 5∫ x^2 dx + ∫ e^2x d(2x)

Answer 15

1/2 ∫ e^2x d(2x) ***

Answer 16

Okay, let's look at taking the integral of x^2. To take the integral of x^2, you ADD ONE to the exponent, so we have x^3
THEN, you multiply by the reciprocal of the exponent. So, you end up with

x^3 / 3 times the coefficient (5) = 5x^3 / 3

Answer 17

ill brb

Answer 18

ok.