Advertisements
Advertisements
Question
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
Advertisements
Solution
`I = int sec^2 x /sqrt(tan^2 x+4) dx.`
`"Let" tan x = t`
`sec^2 xdx = dt`
So, `I = int dt/sqrt(t^2 + 4)`
or, `I = int dt/sqrt(t^2 + 2^2)`
Since, we Know
`int dx/sqrt(x^2 + a^2) = "In" |x + sqrt(a^2 + x^2)| + "C"`
`I = "In" |t + sqrt(t^2 + 4)| + "C"`
`i.e`
`I = "In"|tanx + sqrt(tan^2 x + 4)| + "C"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin2 (2x + 5)
Find the integrals of the function:
cos 2x cos 4x cos 6x
Find the integrals of the function:
sin3 (2x + 1)
Find the integrals of the function:
sin x sin 2x sin 3x
Find the integrals of the function:
`(1-cosx)/(1 + cos x)`
Find the integrals of the function:
tan3 2x sec 2x
Find the integrals of the function:
`1/(sin xcos^3 x)`
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find `int_ (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`
Find: `int_ (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`
Find: `int sin^-1 (2x) dx.`
Evaluate `int tan^8 x sec^4 x"d"x`
Evaluate the following:
`int ("d"x)/(1 + cos x)`
Evaluate the following:
`int sqrt(1 + sinx)"d"x`
Evaluate the following:
`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`
`int (cos^2x)/(sin x + cos x)^2 dx` is equal to
What does integration using trigonometric identities mean?
Which identity is used for the product of sine and cosine?
Which identity is used for \(\sin^3 x\)?
Using \(\cos^2 x = \frac{1+\cos 2x}{2}\), which expression is equivalent to \(\int \cos^2 x\,dx\)?
What is \(\int \cos^2 x\,dx\)?
Applying the product-to-sum identity to \(\sin 2x\cos 3x\) gives which expression?
Which procedure is recommended when an identity can simplify a complicated trigonometric expression?
