Advertisements
Advertisements
Question
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Advertisements
Solution
Let `I = int (cos x)/sqrt(1 + sin x)` dx
Put 1 + sin x = t
cos x dx = dt
∴ `I = int dt/sqrt(1 + t) = (1 + t)^(1/2 +1)/(1/2 + 1) + C`
`= 2 (1 + t)^(1/2) + C`
`= 2 sqrt(1 + sin x + C)`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate `int 1/((2"x" + 3))` dx
`int cos sqrtx` dx = _____________
`int x/(x + 2) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int sin^-1 x`dx = ?
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
