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Integrate with respect to x: i) (2x+3)...

Integrate with respect to x:
i) `(2x+3)^(5)`, ii) `sin2x`, iii) `sec^(2)(4x+5)`, iv) `sec(3x+2)`, v) `tan(2x+1)`, vi) `2^(3x+4)`
vii) `1/(2x+1)` viii) `e^(4x+5)`

Text Solution

Verified by Experts

i) `(2x+3)^(6)/(12)+C`, ii) `-(cos2x)/2+C`, iii) `(tan(4x+5))/(4)+C`
iv) `=1/3ln|sec(3x+2)+tan(3x+2)|+C` , v) `1/2ln|sec(2x+1)|+C`,
vi) `2^(3x+4)/(3ln 2)+C`, vii) `1/2ln |2x+1|+C`, vii) `1/2ln|2x+1|+C`, viii) `(e^(4x+5))/(4)+C`
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Knowledge Check

  • Differentiate the following with respect to x. (i) sin 2x (ii) cos 3x (iii) tan 4x (iv) sin^3x (v) x^2//tan x

    A
    `2 cos 2x`, `- 3 sin 3x`
    B
    `2 cos 2x` , ` 3 sin 3x`
    C
    `2 cos 2x ,` `- 4 sin 3x`
    D
    `2 cos 2x`, ` 3 sinx`

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