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
Evaluate :`intxlogxdx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Write a value of
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
`int "dx"/(9"x"^2 + 1)= ______. `
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
`int logx/(log ex)^2*dx` = ______.
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
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 (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int (log x)/(log ex)^2` dx = _________
`int sqrt(1 + sin2x) dx`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int (cos2x)/(sin^2x) "d"x`
Evaluate `int(3x^2 - 5)^2 "d"x`
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int 1/(sinx.cos^2x)dx` = ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
`int "cosec"^4x dx` = ______.
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
