Advertisements
Advertisements
Question
Evaluate `int (cos 2x + 2sin^2x)/(cos^2x) dx`
Advertisements
Solution
`(cos 2x + 2sin^2x)/(cos^2x)`
`= (cos 2x + (1-cos 2x))/cos^2x` [`cos 2x = 1 - sin^2 x`]
`= 1/cos^2x`
`= sec^2 x`
`:. int (cos^2x + 2sin^2x)/cos^2x` dx = `int sec^2 x dx = tanx + C`
APPEARS IN
RELATED QUESTIONS
Find `int dx/(5 - 8x - x^2)`
Find `int (cos theta)/((4 + sin^2 theta)(5 - 4 cos^2 theta)) d theta`
Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x + \tan x}dx\] .
Prove that `int_0^"a" "f(x)" "dx" = int_0^"a" "f"("a"-"x")"dx"` ,and hence evaluate `int_0^1 "x"^2(1 - "x")^"n""dx"`.
Evaluate the following:
`int sqrt(("a" + x)/("a" - x)) "d"x`
The value of the integral `int_(-1)^2 [x] dx` is
`int (sin^8x - cos^8x)/(1 - 2sin^2x cos^2x) dx` is equal to
`int_0^oo (dx)/((x^2 + a^2)(x^2 + b^2))` is
Evaluate: `int_0^(pi/2) cosx/(( cos x/2 + sin x/2)^3) dx`
If `d/dx f(x) = 2x + 3/x` and f(1) = 1, then f(x) is ______.
Evaluate \[\frac{d}{dx}\left(\int f(x)\,dx\right).\]
Which expression gives the indefinite integral of \[f'(x)\]?
Differentiation and indefinite integration are what type of processes?
If \[\frac{d}{dx}[F(x)]=\frac{d}{dx}[G(x)],\] what follows?
Which formula is the Sum Rule?
Which formula states the General Linearity Rule, where \[k_1,k_2,\ldots,k_n\] are real constants?
What is integration by the method of inspection?
Find an antiderivative of \[\cos 2x.\]
Evaluate \[\int(\sin x+\cos x)\,dx.\]
Evaluate \[\int\operatorname{cosec}x(\operatorname{cosec}x+\cot x)\,dx.\]
Find the antiderivative \[F\] of \[f(x)=4x^3-6\] satisfying \[F(0)=3.\]
