Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
84401	Find the Antiderivative	3/(x^2+3x)	$\frac{3}{x^{2} + 3 x}$
84402	Evaluate the Integral	integral of square root of (x^2)/2 with respect to x	$\int \sqrt{\frac{x^{2}}{2}} d x$
84403	Find the Derivative - d/dy	d/(dy) natural log of x^2+y^2	$\frac{d}{d y} \ln (x^{2} + y^{2})$
84404	Evaluate the Integral	integral of (2x)/(x^2) with respect to x	$\int \frac{2 x}{x^{2}} d x$
84405	Find the Center and Radius	(x-3)^2+(y+1/2)^2=24	${(x - 3)}^{2} + {(y + \frac{1}{2})}^{2} = 24$
84406	Find the Third Derivative	5^x+2x	$5^{x} + 2 x$
84407	Evaluate the Integral	integral of sec(x)^2+2sin(1/4x)-cot(an*5x) with respect to x	$\int \sec^{2} (x) + 2 \sin (\frac{1}{4} x) - \cot (a n \cdot 5 x) d x$
84408	Find the Integral	2/(x^2+1)	$\frac{2}{x^{2} + 1}$
84409	Evaluate the Integral	integral of -(5 cube root of x^2)/3 with respect to x	$\int - \frac{5 \sqrt[3]{x^{2}}}{3} d x$
84410	Evaluate the Integral	integral from 1 to 4 of (s^4-8)/(s^2) with respect to s	$\int_{1}^{4} \frac{s^{4} - 8}{s^{2}} d s$
84411	Evaluate the Limit	limit as x approaches 0 of ((2x+1)^2-1)/x	$lim_{x \to 0} \frac{{(2 x + 1)}^{2} - 1}{x}$
84412	Find the Maximum/Minimum Value	A(t)=300te^(-2.5t)	$A (t) = 300 t e^{- 2.5 t}$
84413	Find the Antiderivative	2^x+x+1	$2^{x} + x + 1$
84414	Find the Derivative - d/dx	d/(dx)-sin(x)	$\frac{d}{d x} - \sin (x)$
84415	Find the Antiderivative	f(x)=2/(x+1)	$f (x) = \frac{2}{x + 1}$
84416	Evaluate the Integral	integral of 2 cube root of sin(2x)cos(2x) with respect to x	$\int 2 \sqrt[3]{\sin (2 x)} \cos (2 x) d x$
84417	Evaluate the Integral	integral of x^3e^(6x^4) square root of (2e^(6x^4)+1)^5 with respect to x	$\int x^{3} e^{6 x^{4}} \sqrt{{(2 e^{6 x^{4}} + 1)}^{5}} d x$
84418	Find the Antiderivative	-csc(x)	$- \csc (x)$
84419	Integrate By Parts	integral of e^(2x)sin(x) with respect to x	$\int e^{2 x} \sin (x) d x$
84420	Evaluate the Summation	sum from i=0 to 4 of 8i-5i^2	$\sum_{i = 0}^{4} 8 i - 5 i^{2}$
84421	Find the Maximum/Minimum Value	f(x)=x^4+8x^3+18x^2+4	$f (x) = x^{4} + 8 x^{3} + 18 x^{2} + 4$
84422	Integrate By Parts	integral from 1 to e of natural log of x with respect to x	$\int_{1}^{e} \ln (x) d x$
84423	Find the Antiderivative	(7x^4+5)/(x^2+1)	$\frac{7 x^{4} + 5}{x^{2} + 1}$
84424	Find the Relative Extrema	f(x)=(x^2-4)^(2/3)	$f (x) = {(x^{2} - 4)}^{\frac{2}{3}}$
84425	Find the Derivative - d/dx	y=(x^3)/12+1/x	$y = \frac{x^{3}}{12} + \frac{1}{x}$
84426	Find dy/dx	y^2+3x^2=y^3-x^3	$y^{2} + 3 x^{2} = y^{3} - x^{3}$
84427	Evaluate the Limit	limit as x approaches infinity of (2x^2+5)/(x^2)	$lim_{x \to \infty} \frac{2 x^{2} + 5}{x^{2}}$
84428	Find the Derivative - d/dx	-5/(6 square root of x^3)	$- \frac{5}{6 \sqrt{x^{3}}}$
84429	Evaluate the Summation	2 sum from k=3 to 8 of 9-2k	$2 \sum_{k = 3}^{8} 9 - 2 k$
84430	Find the Second Derivative	y=-2x^2-1/2x^3+1/5x^-4	$y = - 2 x^{2} - \frac{1}{2} x^{3} + \frac{1}{5} x^{- 4}$
84431	Find the Antiderivative	(4x-1)/((2x-1)^2)	$\frac{4 x - 1}{{(2 x - 1)}^{2}}$
84432	Evaluate the Limit	limit as x approaches infinity of (10^8x^5+10^6x^4+10^4x^2)/(10^9x^6+10^7x^5+10^5x^3)	$lim_{x \to \infty} \frac{10^{8} x^{5} + 10^{6} x^{4} + 10^{4} x^{2}}{10^{9} x^{6} + 10^{7} x^{5} + 10^{5} x^{3}}$
84433	Find Where Increasing/Decreasing	f'(x)=2x^3+12x^2-54x	$f' (x) = 2 x^{3} + 12 x^{2} - 54 x$
84434	Find the Derivative - d/dx	y=-1/2x^4+3x^(5/3)+2x	$y = - \frac{1}{2} x^{4} + 3 x^{\frac{5}{3}} + 2 x$
84435	Find the Third Derivative	y=1/2+1/3x^5-1/3x^2+5/9x	$y = \frac{1}{2} + \frac{1}{3} x^{5} - \frac{1}{3} x^{2} + \frac{5}{9} x$
84436	Find the Absolute Max and Min over the Interval	y=3cos(x) , [0,2pi]	$y = 3 \cos (x)$ , $[0, 2 π]$
84437	Evaluate the Limit	limit as x approaches 2 of -(x^2)/2-x+5/2	$lim_{x \to 2} - \frac{x^{2}}{2} - x + \frac{5}{2}$
84438	Find the Tangent Line at (5,2/5)	f(x)=2/x at (5,2/5)	$f (x) = \frac{2}{x}$ at $(5, \frac{2}{5})$
84439	Find the Second Derivative	x-1/x	$x - \frac{1}{x}$
84440	Find the Maximum/Minimum Value	y=1-3sin(2/3x)	$y = 1 - 3 \sin (\frac{2}{3} x)$
84441	Evaluate the Integral	integral of (x^3+x)/(x+1) with respect to x	$\int \frac{x^{3} + x}{x + 1} d x$
84442	Evaluate the Integral	integral of (-3x^4-6) with respect to x	$\int (- 3 x^{4} - 6) d x$
84443	Find dx/dy	x+2xy-y^2=2	$x + 2 x y - y^{2} = 2$
84444	Find the Derivative - d/dx	(sin(x^2))/(3x)	$\frac{\sin (x^{2})}{3 x}$
84445	Find the Derivative - d/dx	y = fifth root of 5x+2	$y = \sqrt[5]{5 x + 2}$
84446	Find the Derivative - d/dx	natural log of (2x-1)/(x-1)	$\ln (\frac{2 x - 1}{x - 1})$
84447	Find Where Increasing/Decreasing	f(x)=-12 cube root of x	$f (x) = - 12 \sqrt[3]{x}$
84448	Find the Concavity	1/10x^5+2x^4+9x^3	$\frac{1}{10} x^{5} + 2 x^{4} + 9 x^{3}$
84449	Find the Maximum/Minimum Value	y=(e^x)/x	$y = \frac{e^{x}}{x}$
84450	Find the Derivative - d/dx	-( fifth root of x)/2	$- \frac{\sqrt[5]{x}}{2}$
84451	Find dy/dx	y=4arccoth(4x-8)	$y = 4 arccoth (4 x - 8)$
84452	Find dy/dx	y=-cot(2x)	$y = - \cot (2 x)$
84453	Evaluate the Limit	limit as x approaches 3 from the right of (\|x-3\|)/(3-x)	$lim_{x \to 3^{+}} \frac{\| x - 3 \|}{3 - x}$
84454	Find the Antiderivative	1/( square root of x)+ cube root of x	$\frac{1}{\sqrt{x}} + \sqrt[3]{x}$
84455	Find dy/dx	a^3y=x^2(2a^2-x^2)	$a^{3} y = x^{2} (2 a^{2} - x^{2})$
84456	Find the Antiderivative	f(x)=1/( square root of x+3)	$f (x) = \frac{1}{\sqrt{x + 3}}$
84457	Find the Derivative - d/dx	y=6pi^3-8pi^2+24	$y = 6 π^{3} - 8 π^{2} + 24$
84458	Find dy/dx	y=x^3(2x-5)^4	$y = x^{3} {(2 x - 5)}^{4}$
84459	Find Where Increasing/Decreasing	f(x)=x^3-2x^2+x	$f (x) = x^{3} - 2 x^{2} + x$
84460	Find the Derivative - d/df	f^2(x)	$f^{2} (x)$
84461	Evaluate the Limit	limit as x approaches infinity of 2+5x+x^2	$lim_{x \to \infty} 2 + 5 x + x^{2}$
84462	Find the Derivative - d/dx	square root of xe^(-x)	$\sqrt{x} e^{- x}$
84463	Evaluate the Integral	integral from 0 to 1 of (x^16+16^x) with respect to x	$\int_{0}^{1} (x^{16} + 16^{x}) d x$
84464	Evaluate the Integral	integral of (10 cube root of 5x-2)/3 with respect to x	$\int \frac{10 \sqrt[3]{5 x - 2}}{3} d x$
84465	Integrate Using u-Substitution	integral of e^(sin(x))cos(x) with respect to x	$\int e^{\sin (x)} \cos (x) d x$
84466	Find the Derivative - d/dh	(f(2+h)-f(2))/h	$\frac{f (2 + h) - f (2)}{h}$
84467	Find the Inflection Points	-3/20x^5+11x^3	$- \frac{3}{20} x^{5} + 11 x^{3}$
84468	Find the Center and Radius	x^2+y^2+z^2-8x+8z+16=0	$x^{2} + y^{2} + z^{2} - 8 x + 8 z + 16 = 0$
84469	Find the Maximum/Minimum Value	f(x)=sin(2x)	$f (x) = \sin (2 x)$
84470	Evaluate the Integral	integral from 1 to 27 of cube root of x-1/x with respect to x	$\int_{1}^{27} \sqrt[3]{x} - \frac{1}{x} d x$
84471	Evaluate from the Right	limit as x approaches 0 of (x-1)/(x+1)	$lim_{x \to 0} \frac{x - 1}{x + 1}$
84472	Find the Antiderivative	f(x)=2sin(x/2)^2	$f (x) = 2 \sin^{2} (\frac{x}{2})$
84473	Evaluate the Limit	limit as x approaches 0 of (1+arctan(x))^(1/x)	$lim_{x \to 0} {(1 + \arctan (x))}^{\frac{1}{x}}$
84474	Find the Slope	-2/1	$- \frac{2}{1}$
84475	Evaluate the Limit	limit as x approaches 3 of ((x-2)^2-(x-4)^2)/(x-3)	$lim_{x \to 3} \frac{{(x - 2)}^{2} - {(x - 4)}^{2}}{x - 3}$
84476	Find the Derivative - d/dx	d/(dx)(1/(x^3)-1/x+x^2)	$\frac{d}{d x} (\frac{1}{x^{3}} - \frac{1}{x} + x^{2})$
84477	Evaluate the Integral	integral of ((7x^6)/(x^7+2)) with respect to x	$\int (\frac{7 x^{6}}{x^{7} + 2}) d x$
84478	Find the Derivative - d/dx	y=4/( square root of -x^2+2x-5)	$y = \frac{4}{\sqrt{- x^{2} + 2 x - 5}}$
84479	Evaluate the Integral	integral of x^(1/3)(x^(4/3)+9)^8 with respect to x	$\int x^{\frac{1}{3}} {(x^{\frac{4}{3}} + 9)}^{8} d x$
84480	Find the Maximum/Minimum Value	Find the minimum value of the parabola y=x^2	Find the minimum value of the parabola $y = x^{2}$
84481	Evaluate the Limit	limit as x approaches c of square root of 12*f(x)	$lim_{x \to c} \sqrt{12 \cdot f (x)}$
84482	Find the Second Derivative	e^(sin(x))	$e^{\sin (x)}$
84483	Find the Antiderivative	1+1/x	$1 + \frac{1}{x}$
84484	Find the Linearization at t(x)=x³-5x²-9x+45	t(x)=x^3-5x^2-9x+45 , x-5	$t (x) = x^{3} - 5 x^{2} - 9 x + 45$ , $x - 5$
84485	Find the Antiderivative	x^2*e^(x^3)	$x^{2} \cdot e^{x^{3}}$
84486	Evaluate the Limit	limit as x approaches 0 of (x^2sin(x)+cos(x)+x-1)/(x^2-2x)	$lim_{x \to 0} \frac{x^{2} \sin (x) + \cos (x) + x - 1}{x^{2} - 2 x}$
84487	Integrate Using u-Substitution	integral of tan(x)^3 with respect to x	$\int \tan^{3} (x) d x$
84488	Find dy/dx	cos(xy)=y-1	$\cos (x y) = y - 1$
84489	Find dx/dy	y=x+1/x	$y = x + \frac{1}{x}$
84490	Find dy/dx	-x^2+y^2=-3y	$- x^{2} + y^{2} = - 3 y$
84491	Find the Second Derivative	e^x+e^(-x)	$e^{x} + e^{- x}$
84492	Find the Derivative - d/dx	y=((2x^4-1)(bx^5+3))/(x^5)	$y = \frac{(2 x^{4} - 1) (b x^{5} + 3)}{x^{5}}$
84493	Integrate By Parts	integral of 2xsin(x) with respect to x	$\int 2 x \sin (x) d x$
84494	Evaluate Using L'Hospital's Rule	limit as r approaches 0 from the right of -11(r/3) natural log of r/5	$lim_{r \to 0^{+}} - 11 (\frac{r}{3}) \ln (\frac{r}{5})$
84495	Find the Maximum/Minimum Value	f(x)=1/3x^3-2x^2-5x	$f (x) = \frac{1}{3} x^{3} - 2 x^{2} - 5 x$
84496	Evaluate the Integral	integral of 1/(x square root of 4x^2+1) with respect to x	$\int \frac{1}{x \sqrt{4 x^{2} + 1}} d x$
84497	Find the Derivative - d/dx	d/(dx)cos(2x)	$\frac{d}{d x} \cos (2 x)$
84498	Find the Derivative - d/dx	(3-5x)/(2x^2-3)	$\frac{3 - 5 x}{2 x^{2} - 3}$
84499	Evaluate the Integral	integral from 1 to 4 of (x^2+x) with respect to x	$\int_{1}^{4} (x^{2} + x) d x$
84500	Evaluate the Limit	limit as x approaches negative infinity of (2x^2-7x^4)/(9x^2+5x-6)	$lim_{x \to - \infty} \frac{2 x^{2} - 7 x^{4}}{9 x^{2} + 5 x - 6}$