33. Prove for a > 0: dx x2 + a 1 tan Ja

Q: Evaluate the definite integral.

A: We have to evaluate the integration ∫0π3sec32xtanxdx

Q: sec 3x tan² 3x dx

A:

Q: Find the indefinite integral.

A: We have to solve the indefinite integral: ∫tan x3 sec2 x dx Solving the integral by substitution…

Q: Evaluate the integral. ∫0 π/3 tan5 x Sec4 x dx

A:

Q: Evaluate the indefinite integral

A:

Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

A:

Q: Evaluate the integral.  integral  sec  x  tan  4 x  dx

A:

Q: Let y tan 1)2x then dy/dx at x-1 is

A:

Q: f(x)% 3D tanh In(2x) is equivalent to

A:

Q: Evaluate the integral.  integral  sec 3 x  tan  4 x  dx

A: Given

Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: evaluate the indefinite integral.

A:

Q: Find the indefinite integral ∫ 3√(tan x) sec2 x dx

A: ∫tanx3sec2x dx Now put tanx=t⇒sec2x=dtdx⇒sec2x  dx=dt

Q: Find the integral m tanx 1+x?

A:

Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

Q: Show that (In kx) dx (In x), where x > 0 and k is a positive dx real number.

A: ddxln kx=ddxln x, where x>0 & k is a positive real number.

Q: Evaluate the indefinite integral: ∫sec x tan x dx

A: Given indefinite integral is ∫secxtanxdx

Q: Find integral.

A:

Q: Use thě substitution a = 7 tan(0) to evaluate the indefinite integral 40dx x²Væ² + 49 +C

A: Substitute x=7tanθ After differentiating, dx=7sec2θdθ

Q: Evaluate the indefinite integral. tan (x) sec2(x) dx = +C.

A: SOLUTION-

Q: Evaluate the integral. 7 2ex sinh(x) + cosh(x) dx

A: To integrate ∫-772exsinh(x)+cosh(x)dx Apply the constant multiple rule: ∫cf(x)dx=c∫f(x)dx . Here c =…

Q: Use the substitution x = 5 tan(0) to evaluate the indefinite integral 40 dx x² Vx² + 25

A:

Q: Evaluate the indefinite integral.

A: Consider the given integral I=∫sec3x·tanx dx

Q: Evaluate the integral. integral 0  to pie /2     sin 3x  cos 2x dx

A: Consider,

Q: Find the indefinite integral using the substitution x = 2 tan θ.

A:

Q: Evaluate the integral. 6. 2ex dx sinh(x) + cosh(x)

A: Consider the given integral.

Q: Evaluate the indefinite integral. (tan- x) dx = || 1+x?

A: Given integral is ∫tan-1x51+x2dx

Q: Find the indefinite integral ∫sec2 (x/2) tan (x/2) dx

A: Given: I=∫sec2x2tanx2dx

Q: Find the indefinite integral. ∫arctan x dx

A:

Q: Use Property 8 to estimate the value of the integral.

A:

Q: Find dy Ldx For the following (Jy)' =(In tan x)(x") ( sin x)"

A:

Q: Evaluate the integral: S(sec(x) tan(x) + 4•x)dx .

A: The given integral,    ∫secx.tanx+4.xdx

Q: Evaluate the integral. sec x tanx dx 2 + sec x -In |2 + sec x| + C O In 12 + sec x| + C 2 In Isec x|…

A:

Q: evaluate using the integral 34. tanx sec x dx II Expand

A:

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

A:

Q: Find the product of the integral 1- L sin(x)ecos(x)-2y dxdy

A:

Q: 20. Verify by differentiation that finx dx = x(In x-1) + C, then use appropriate changes of…

A:

Q: Evaluate the indefinite integral.

A: It is required to evaluate the indefinite integral:

Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: Find the indefinite integral. tan“ X dx sec x

A:

Q: Evaluate the integral. |3 tan Sx [ 31 tan x sec "x dx 5. 31 tan x sec x dx = sec *x d

A:

Q: Find where where y = V5x + sech¬1 x + In (tanh(x² + 3)). dx

A:

Q: integral from 0 to pie over 4 of sin^2 (4x) cos^2 (2x) dx

A:

Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…

Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

A:

Q: Find when 4= SINX Thuen dy (sinx) (ar f(s wheve for 0<x< M2 tanx taux a=?

A:

Q: (a) Evaluate the integral t tanx dx by using the reduction formula of tangent function.

A: