हिंदी

Write a Value of ∫ Tan 6 X Sec 2 X D X - Mathematics

Advertisements
Advertisements

प्रश्न

Write a value of

\[\int \tan^6 x \sec^2 x \text{ dx }\] .
योग

उत्तर

Let I= \[\int\] tan6 x . sec2 x dx

Let tan x = t
sec2 x dx = dt
\[\therefore I =\]\[\int\] t6 . dt

\[= \frac{t^7}{7} + C\]
\[ = \frac{\tan^7 x}{7} + C \left( \because t = \tan x \right)\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 19: Indefinite Integrals - Very Short Answers [पृष्ठ १९७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Very Short Answers | Q 6 | पृष्ठ १९७

संबंधित प्रश्न

Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`


Integrate the functions:

`xsqrt(1+ 2x^2)`


Integrate the functions:

`(1+ log x)^2/x`


`(10x^9 + 10^x log_e 10)/(x^10 + 10^x)  dx` equals:


Evaluate : `∫1/(3+2sinx+cosx)dx`


\[\int\sqrt{3 + 2x - x^2} \text{ dx}\]

Write a value of

\[\int e^x \sec x \left( 1 + \tan x \right) \text{ dx }\]

Write a value of\[\int \cos^4 x \text{ sin x dx }\]


Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]


Write a value of\[\int\frac{\cos x}{\sin x \log \sin x} dx\]

 


Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .


The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is


Evaluate the following integrals : `int cos^2x.dx`


Integrate the following functions w.r.t. x : `(logx)^n/x`


Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`


Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`


Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`


Integrate the following functions w.r.t. x :  tan 3x tan 2x tan x


Integrate the following functions w.r.t. x : sin5x.cos8x


Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`


Evaluate `int (1 + "x" + "x"^2/(2!))`dx


Evaluate `int (3"x"^2 - 5)^2` dx


Evaluate the following.

`int (1 + "x")/("x" + "e"^"-x")` dx


Evaluate the following.

`int 1/("x" log "x")`dx


Evaluate the following.

`int 1/(sqrt"x" + "x")` dx


Evaluate the following.

`int 1/(x(x^6 + 1))` dx 


Evaluate `int "x - 1"/sqrt("x + 4")` dx


Evaluate: `int sqrt(x^2 - 8x + 7)` dx


`int 1/(cos x - sin x)` dx = _______________


General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)


`int(log(logx) + 1/(logx)^2)dx` = ______.


`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.


Evaluate `int(1 + x + x^2/(2!) )dx`


Evaluate.

`int(5"x"^2 - 6"x" + 3)/(2"x" - 3)  "dx"`


Evaluate the following.

`int 1/(x^2 + 4x - 5)  dx`


Evaluate `int(1 + x + x^2/(2!))dx`


`int dx/((x+2)(x^2 + 1))`    ...(given)

`1/(x^2 +1) dx = tan ^-1 + c`


Evaluate:

`int(cos 2x)/sinx dx`


Evaluate `int (1 + "x" + "x"^2/(2!))`dx


If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×