Question

Hello Everyone :) Just came across some hard integrals and need help take your time ! :)

Answer 1

\[\int\limits_{0}^{1}\sqrt{\log_{2}(x+1)}+2^{x^2}dx\]

Answer 2

\[\int\limits_{1}^{\infty}\frac{ 1-x+lnx }{ x(1+x)^2\ln^2x}\]

Answer 3

\[\int\limits_{0}^{\pi/2}\frac{ x^2\log^2(sinx) }{ sin^2x }dx\]

Answer 4

and ya there is dx in the second part i forgot to add it can anyone help me solve these 3 integrals? and please do not use online integral calculator like wolfram and etc they just give out the direct answer and that answer is too confusing in form of ' i ' and 'e' and 'square roots' can someone teach me how to integrate these questions ? i have tried different substitution but it doesn't work and there is no typo in the question these are the correct question's

Answer 5

\[\int\limits e ^{-x^2} dx\]

Answer 6

@Photon336 @zepdrix @marcelie @sweetburger

Answer 7

nevermind the last one i found it out can you guys help me with the above three and if you are curious the answer to the last one is
\[\frac{ \sqrt{\pi}erf(x) }{ 2 }+C\]

Answer 8

:O lool is this calculus 1?

Answer 9

naa :P its beyond 1 and 2

Answer 10

@ganeshie8

Answer 11

oh then nvm lmao im in calculus 1 D:

Answer 12

Sorry @ijlal this is way beyond me lol.

Answer 13

haha :P sorry fellas i didn't know thanks for your concern though :) @marcelie @sweetburger

Answer 14

yeh no problem but ill just watch whoever solves it x)

Answer 15

okie dokie :D

Answer 16

@welshfella @mathmale @Preetha @Mehek14

Answer 17

lemme see what i can come up with.

Answer 18

sure :) @jtug6

Answer 19

Yeah this is like, really, really nasty hahahaha im only in calc 3. but yeah this is awful lol. sorry :3

Answer 20

haha no problem thanks for trying though :)

Answer 21

have you tried integrating by parts?

Answer 22

also the first one can be split into the sum of two integrals over addition

Answer 23

this question is till here? lool

Answer 24

i have tried every method i could but didnt seem to get a final answer always got stuck , even tried to integrate it with respective to using power series any help please would be appreciated any link of any website or tag some one who can help me with this

Answer 25

@god

Answer 26

I can attempt the second part of the first integral, which explains the results we get from Wolfram:
let
\(y'=2^{x^2}\)
change base 2 to base e (writing \(log(x)\equiv log_e(x)\) )
\(y'=e^{log(2)x^2}\)
integrate,
\(y=\int e^{log(2)x^2}dx\)
which when applied to the result given earlier for \(\int e^{-x^2}dx\)
gives
\(\Large -\frac{\sqrt{\pi}(i) erf(i \sqrt{log(2)} x)}{2\sqrt{log(2)}}\)

Answer 27

@mathmate thanks buddy really helped alot :)

Answer 28

Wish I could do more! :(

Answer 29

that hint was great though looked up into on youtube and i got my solutions for my answer's :) thank you !

Answer 30

Glad it helped. You work with tough problems, as you can see by all the previous comments! :)