Advertisements
Advertisements
Questions
Integrate the following function w.r.t. x:
x9.sec2(x10)
Evaluate:
`intx^9 . sec^2 (x^10) dx`
Advertisements
Solution
Let I = `int x^9 .sec^2(x^10).dx`
Put x10 = t
∴ 10x9dx = dt
∴ x9dx = `(1)/(10)dt`
∴ I = `int sec^2t.dt/(10)`
= `1/10 int sec^2t dt`
= `(1)/(10)tan t+ c`
= `(1)/(10)tan(x^10) + c`
RELATED QUESTIONS
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
cot x log sin x
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
`int "dx"/(9"x"^2 + 1)= ______. `
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
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 : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate: `int "e"^sqrt"x"` dx
`int x/(x + 2) "d"x`
`int x^3"e"^(x^2) "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int(5x + 2)/(3x - 4) dx` = ______
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
