Question

Hi, please solve this below antiderivatives ( integration) questions. Thanks

Find the antiderivative using proper symbolism ( BIG S and dx) Show detail steps

1- ( sec x ) ^ 2 tanx

2- 3 ^ 1/2 - 4 x ^ -2

3- ( 2x ^ 2 - 8x ) ( 2x -4

4- sin 5x cos5x

5- ( 2- x) ^ 3/5

6- x ^ 3 - x ^ -3

7- e ^2

Answer 1

17 I = S(secr)? tand dr Slet Seate & secretanddu a dd 11 . - 2 +1 - 2 +1 Put the value of t, we get I = (sec page - Secret 2) I = S (2² - 4x²) dx = foden af Kja a Bora 4 x 2 + & Son & 4 glass 3 I = $(22? - SM) (2x-4) 2x = (4x² - 16 x ² – 8 r² + 32x) dx = S(A² – 24² 432x) dx 54mm - 24 min + B2 x to 4

4 I = (sin 5%) (Cos5r) d Sheit sinke at 5 cosbadnadt - Cassa) du = at & c Put the value of to sinkt, a t 11 = $int Sx+c do 5) I=S (2-w7d phet (2-) = d. 2 s (a da) Y = - &*st to - - oda a da - daardt - tc 3 dl to la gly - + + 815 419 1 = -2 4 + c d 6) I = S(x3 - x x & Selte a fin de 17

7 Ia Jezde Is eextc) s