Advertisements
Advertisements
प्रश्न
Integrate the following function w.r.t. x:
x9.sec2(x10)
Evaluate:
`intx^9 . sec^2 (x^10) dx`
Advertisements
उत्तर
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`
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`e^(2x+3)`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
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 : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate `int 1/((2"x" + 3))` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int x^2/sqrt(1 - x^6)` dx = ________________
`int cos sqrtx` dx = _____________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int logx/x "d"x`
`int x^x (1 + logx) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int(log(logx))/x "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
Evaluate `int(3x^2 - 5)^2 "d"x`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int cos^3x dx` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate `int (1)/(x(x - 1))dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
