17. Find the integral of ((x^4)/((x^2)+7))dx

Q: Find the general indefinite integrals integral of x(x3+2)2dx integral of 3x2(x3+1)4dx

A: The given integral of  xx3+22dx     =    ∫xx3+22dx = ∫xx32+2(x3).2+22dx  = ∫x7+4x4+4xdx =…

Q: How to evaluate the integral of [(dx)/(9-x2)(3/2)]

A:

Q: 6. Estimate the integral: ܐܢ ex. dx

A:

Q: the integral of (4x^3-10x^2-x-15)/(x^4-3x^3)dx

A:

Q: Determine the indefinite integral below. S12x+ 5°dx. |(12x+5)°dx= [

A:

Q: Use any method to evaluate the integrals ∫ 2x - 2-x/2x + 2-x dx

A:

Q: Evaluate the integrals ∫sec6 x dx

A:

Q: calculate the integral.

A:

Q: Compute integral01  x * cubed root of 1+x^2  dx

A:

Q: Evaluate the improper integral, 5 if exists : dx (5 – x)3

A:

Q: Use any method to evaluate the integral. 20 dx (100x2 + 1) 2 20 dx (100x2 + 1) 2

A:

Q: Find the indefinite integral. 1 (12x°) dx 4 + 3x* 4 1 (12x°) dx = 4 4 + 3x

A:

Q: Evaluate the integrals ∫4 cosh (3x - ln 2) dx

A: Given: I=∫4cosh3x-ln2dx here, 4cosh is constant, so it will come out from integral

Q: 3 Estimate the integral 1 dx by Simpson's rule using n= 8. Vx3 + 5

A: Given that a integration and ask estimate value use Simpson rule when n= 8. In Simpson rule we can…

Q: Compute. integral (1) / (square root 1 + x2)3 dx

A:

Q: S 10x(1 - x)5 dx

A:

Q: Evaluate the integral * In 2 tanh 2x dx

A: We have to find Integral of given function.

Q: Find the Indefinite Integral by making a change of varlab of Integration.) dx

A: Given: I=∫xx-6dx    ....1 Let, u=x-6⇒x=u+6 Now differentiate on both sides with respect to x.…

Q: Find the integral. In 8x dx

A: I=∫ ln 8xx dxln 8x =t18x(8) dx = dtdxx =dt

Q: s/4 dx 2- 1+tanx 3.

A:

Q: Find the integral

A: To integrate ∫ln|4x+5|dx, use the substitution method and consider 4x+5 as t. Differentiate both…

Q: 4) 2²e*dx (Improper Int.)

A:

Q: Calculate the indefinite integral S (2Vx3+3)(2Vx3 – 3) dx

A:

Q: Evaluate the integrals ∫6 cosh (x/2 - ln 3) dx

A: ∫6coshx2-ln3 dx Put, x2-ln3=t⇒12-0=dtdx⇒12dx=dt⇒dx=2 dt

Q: Find the indefinite intergral of: Integral cube root of x^2 - (1/x^2) dx

A: Consider the given integral.

Q: Compute.  integral ln2x/x dx

A:

Q: Calculate the integral of x(1+ 3x)° dx .

A:

Q: Find the integral [(3x² – x) In(3x)dx .

A: Given query is to solve the integral.

Q: Evaluate the integral of cosh2x(sinh 2x)^2 dx

A: ∫cosh2xsinh2x2dx

Q: Evaluate the definity integral  from 0-4 (x-3)(x-5)dx

A: Evaluate the integral ∫04x-3x-5 dx.

Q: Evaluate the indefinite integral. ex V 36 + ex dx

A: Given: ∫ex36+exdx

Q: Find the indefinite integral: Integral of (x3 - 3x divided by 3x2) dx

A:

Q: Evaluate the integral. 12x – 9 - dx = x2 + lx – 6 4 -

A: Given, Evaluate ∫4512x-9x2+1· x-6dx

Q: Match the integral expression on the left to an equal expression on the right. Ssin(3x)sin(4x)dx -…

A: Let's find.

Q: Evaluate the integrals in ∫(ln x)3/2x dx

A: Consider the given integral, ∫lnx32xdx use the substitution, t=lnxx=etdx=etdt so, the integral…

Q: Find the indefinite integral ∫ (x2 + 2x + 3) / (x3 + 3x2 + 9x)   dx

A: To evaluate ∫x2+2x+3x3+3x2+9xdx

Q: compute the integral of    "(sinx * tanhx ) / ln(x+0.01)" from 1 to 5 to at least 6 significant…

A: Given :  ∫15sinxtanhxlog(x+0.01)dx

Q: 4x √x² - 1 2 s dx

A: Solve the integration

Q: In 2 tanh 2x dx

A:

Q: Use Property 8 of integrals to estimate the value of the integral. ∫20(x3-3x+3)dx.

A:

Q: Evaluate the integral of ex*+1 2x dx.

A:

Q: 4) Reverse the order of integration in 2 2x x' dydx 0 x2 and evaluate the integral as an x-simple…

A: To reverse the order of the below integration. ∫02∫x22xx3dydx

Q: Evaluate integral of (4x - 15) dx over x^2 - 4x +13

A: To find: ∫4x - 15x2 - 4x +13dx

Q: Evaluate the indefinite integral. ex. 1 + ex dx + C

A: For the given functions indefinite integrals are determined

Q: Use Property 8 of integrals to estimate the value of    ∫13 √ (x2  + 3 ) dx

A:

Q: ∫−∞0 (2x/(x2+5)3) dx

A: Given,   ∫−∞0 (2x/(x2+5)3) dx

Q: Use Simpson's Rule with n = 4 steps to estimate the integral. 5) dx

A:

Q: Compute integral x^2cos(x^3+3) dx

A: Given : ∫x2cosx3 + 3dx

Q: integral In(2x +1) dx

A: Given To Evaluate ∫ln(2x+1)dx

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.