Advertisements
Advertisements
प्रश्न
Write a value of
Advertisements
उत्तर
Let I= \[\int\] tan6 x . sec2 x dx
sec2 x dx = dt
\[= \frac{t^7}{7} + C\]
\[ = \frac{\tan^7 x}{7} + C \left( \because t = \tan x \right)\]
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
tan2(2x – 3)
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate `int (5"x" + 1)^(4/9)` dx
`int sqrt(x^2 + 2x + 5)` dx = ______________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int x/(x + 2) "d"x`
`int sec^6 x tan x "d"x` = ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
`int cos^3x dx` = ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
