Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
80501	Integrate Using u-Substitution	integral of (2x)/(x^2+1) with respect to x	$\int \frac{2 x}{x^{2} + 1} d x$
80502	Evaluate the Summation	sum from i=1 to 7 of (3i-2)^2	$\sum_{i = 1}^{7} {(3 i - 2)}^{2}$
80503	Find the Inflection Points	f(x)=x+3(x-1)^(1/3)	$f (x) = x + 3 {(x - 1)}^{\frac{1}{3}}$
80504	Find the Antiderivative	2xcos(x^2)	$2 x \cos (x^{2})$
80505	Find the Third Derivative	y=e^x	$y = e^{x}$
80506	Evaluate the Limit	limit as x approaches 0 from the right of (1/x)^x	$lim_{x \to 0^{+}} {(\frac{1}{x})}^{x}$
80507	Find the Derivative - d/dx	(x+2)^5(x-3)^4	${(x + 2)}^{5} {(x - 3)}^{4}$
80508	Evaluate the Limit	limit as x approaches 4 of (2 square root of x-2)/(2x-4)	$lim_{x \to 4} \frac{2 \sqrt{x} - 2}{2 x - 4}$
80509	Find the Antiderivative	2sin(x)+x^2	$2 \sin (x) + x^{2}$
80510	Find the Integral	(4e^2)/(x^-3)	$\frac{4 e^{2}}{x^{- 3}}$
80511	Find the Second Derivative	y=xcos(5x)-sin(x)^2	$y = x \cos (5 x) - \sin^{2} (x)$
80512	Evaluate the Limit	limit as x approaches 0 of (1/x)^x	$lim_{x \to 0} {(\frac{1}{x})}^{x}$
80513	Find the Third Derivative	y=ax^4+bx^2+c	$y = a x^{4} + b x^{2} + c$
80514	Find the Antiderivative	2x^(2/3)-5x^3	$2 x^{\frac{2}{3}} - 5 x^{3}$
80515	Evaluate the Integral	integral of 4/(x^3)-5x square root of x with respect to x	$\int \frac{4}{x^{3}} - 5 x \sqrt{x} d x$
80516	Find the Upper and Lower Bounds	f(x)=x^4-4x^3+9x^2-x-14	$f (x) = x^{4} - 4 x^{3} + 9 x^{2} - x - 14$
80517	Find the Derivative - d/dx	- square root of 5x	$- \sqrt{5 x}$
80518	Find the Antiderivative	x/( square root of 2x+1)	$\frac{x}{\sqrt{2 x + 1}}$
80519	Evaluate the Limit	limit as x approaches infinity of (5x-28x^3)/(5x^2-14x^3-9)	$lim_{x \to \infty} \frac{5 x - 28 x^{3}}{5 x^{2} - 14 x^{3} - 9}$
80520	Evaluate the Limit	limit as x approaches -1 of (x^2-3x-4)/(x^2+2x-3)	$lim_{x \to - 1} \frac{x^{2} - 3 x - 4}{x^{2} + 2 x - 3}$
80521	Find the Maximum/Minimum Value	-2cos(5/4x)	$- 2 \cos (\frac{5}{4} x)$
80522	Find the Percentage Rate of Change	s(t)=0.65(0.48)^t	$s (t) = 0.65 {(0.48)}^{t}$
80523	Find the Antiderivative	e^x+1	$e^{x} + 1$
80524	Find the Inflection Points	f(x)=-3/20x^5+11x^3	$f (x) = - \frac{3}{20} x^{5} + 11 x^{3}$
80525	Find the Antiderivative	(sin(x))/(12+cos(x))	$\frac{\sin (x)}{12 + \cos (x)}$
80526	Find the Center and Radius	(x-2)^2+y^2-25=0	${(x - 2)}^{2} + y^{2} - 25 = 0$
80527	Evaluate the Limit	limit as x approaches infinity of ((2x+1)(4x-1)^2)/((2x+3)^3)	$lim_{x \to \infty} \frac{(2 x + 1) {(4 x - 1)}^{2}}{{(2 x + 3)}^{3}}$
80528	Find the Antiderivative	log of x	$\log (x)$
80529	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/x-cos(5x)	$lim_{x \to 0} \frac{\sin (2 x)}{x} - \cos (5 x)$
80530	Evaluate the Limit	limit as x approaches 2 from the right of x^3-2x^2-3	$lim_{x \to 2^{+}} x^{3} - 2 x^{2} - 3$
80531	Evaluate the Limit	limit as x approaches infinity of ( square root of 4x^2+1)/(x-2)	$lim_{x \to \infty} \frac{\sqrt{4 x^{2} + 1}}{x - 2}$
80532	Find the Derivative - d/dx	(1- natural log of x)/(x^2)	$\frac{1 - \ln (x)}{x^{2}}$
80533	Find the Second Derivative	f(x)=e^x+100e+8x^4+49	$f (x) = e^{x} + 100 e + 8 x^{4} + 49$
80534	Find dy/dx	y=(x^2+5)(3x+1)	$y = (x^{2} + 5) (3 x + 1)$
80535	Find the Antiderivative	f(x)=x^2+2/(x^2)	$f (x) = x^{2} + \frac{2}{x^{2}}$
80536	Integrate Using u-Substitution	integral from 0 to 1 of (e^x)/(1+e^(2x)) with respect to x	$\int_{0}^{1} \frac{e^{x}}{1 + e^{2 x}} d x$
80537	Evaluate the Limit	limit as x approaches c of -2/infinity	$lim_{x \to c} \frac{- 2}{\infty}$
80538	Find the Antiderivative	f(x)=x^5+8x^3- square root of 5	$f (x) = x^{5} + 8 x^{3} - \sqrt{5}$
80539	Find the Concavity	f(x)=-1/3x^3+x^2	$f (x) = - \frac{1}{3} x^{3} + x^{2}$
80540	Find the Antiderivative	f(x)=-1/(x^3)	$f (x) = - \frac{1}{x^{3}}$
80541	Evaluate the Integral	integral from -3 to 4 of [y-(y^2-12)] with respect to y	$\int_{- 3}^{4} [y - (y^{2} - 12)] d y$
80542	Find the Antiderivative	x/2-4x^3-x^4	$\frac{x}{2} - 4 x^{3} - x^{4}$
80543	Find the Inflection Points	f(x)=1/15x^6+x^5+25/6x^4	$f (x) = \frac{1}{15} x^{6} + x^{5} + \frac{25}{6} x^{4}$
80544	Find the Antiderivative	x^x	$x^{x}$
80545	Find the Slope of the Tangent Line at (4,2)	y = square root of x , (4,2)	$y = \sqrt{x}$ , $(4, 2)$
80546	Evaluate the Limit	limit as x approaches 2 of cube root of -x+4	$lim_{x \to 2} \sqrt[3]{- x + 4}$
80547	Evaluate the Integral	integral of 3u1/2 with respect to u	$\int 3 u \frac{1}{2} d u$
80548	Evaluate the Integral	integral from negative infinity to 0 of (x*e^x)/((x+1)^2) with respect to x	$\int_{- \infty}^{0} \frac{x \cdot e^{x}}{{(x + 1)}^{2}} d x$
80549	Find the Derivative - d/dx	x^(2 square root of 3)	$x^{2 \sqrt{3}}$
80550	Evaluate the Integral	integral from -2 to 2 of \|x^2-4\| with respect to x	$\int_{- 2}^{2} \| x^{2} - 4 \| d x$
80551	Evaluate the Integral	integral of 4x(5^(x^2)) with respect to x	$\int 4 x (5^{x^{2}}) d x$
80552	Find the Maximum/Minimum Value	y=3sin(2x-pi/2)+1	$y = 3 \sin (2 x - \frac{π}{2}) + 1$
80553	Find the Antiderivative	1/(x(x+2))	$\frac{1}{x (x + 2)}$
80554	Find the Antiderivative	f(x)=1/(sin(x)^2)	$f (x) = \frac{1}{\sin^{2} (x)}$
80555	Evaluate the Integral	integral from 0 to 2 of [7/(sin(x)^2+cos(x)^2)-4e] with respect to x	$\int_{0}^{2} [\frac{7}{\sin^{2} (x) + \cos^{2} (x)} - 4 e] d x$
80556	Find the Derivative - d/dX	XD	$X D$
80557	Find Where Increasing/Decreasing	h(x)=6x^5-15x^4+10x^3	$h (x) = 6 x^{5} - 15 x^{4} + 10 x^{3}$
80558	Find dy/dx	y=1+2xe^y	$y = 1 + 2 x e^{y}$
80559	Find the Tangent Line at (-1,0)	x^2y^2-2xy+x^2=1 , (-1,0)	$x^{2} y^{2} - 2 x y + x^{2} = 1$ , $(- 1, 0)$
80560	Find the Antiderivative	f(x)=1/(x^2)-2/(x^4)	$f (x) = \frac{1}{x^{2}} - \frac{2}{x^{4}}$
80561	Find the Antiderivative	1/(x^3-x)	$\frac{1}{x^{3} - x}$
80562	Find the Antiderivative	(sin(x))/(cos(x))	$\frac{\sin (x)}{\cos (x)}$
80563	Integrate Using u-Substitution	integral of 18t^2(t^3+1)^5 with respect to t	$\int 18 t^{2} {(t^{3} + 1)}^{5} d t$
80564	Find the Derivative - d/dx	1/( square root of g(2x))	$\frac{1}{\sqrt{g (2 x)}}$
80565	Find the Antiderivative	-3x^-4+10x^(2/3)-7x	$- 3 x^{- 4} + 10 x^{\frac{2}{3}} - 7 x$
80566	Find the Maximum/Minimum Value	x^4(x-2)(x+3)	$x^{4} (x - 2) (x + 3)$
80567	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (6e^(4x)-2e^(3x)-4)/(sin(2x))	$lim_{x \to 0} \frac{6 e^{4 x} - 2 e^{3 x} - 4}{\sin (2 x)}$
80568	Find the Derivative - d/dx	y=4/((x^3+9)^5)	$y = \frac{4}{{(x^{3} + 9)}^{5}}$
80569	Find the Antiderivative	3 square root of x-2 cube root of x	$3 \sqrt{x} - 2 \sqrt[3]{x}$
80570	Find the Derivative - d/dy	(d^2y)/(dx^2)	$\frac{d^{2} y}{d x^{2}}$
80571	Evaluate the Integral	integral of ((2x^3+x^2-3x)/x) with respect to x	$\int (\frac{2 x^{3} + x^{2} - 3 x}{x}) d x$
80572	Find the Derivative - d/dx	y = natural log of sinh(3x)	$y = \ln (\sinh (3 x))$
80573	Evaluate Using Summation Formulas	sum from i=1 to n of (3i-1)^2	$\sum_{i = 1}^{n} {(3 i - 1)}^{2}$
80574	Find the Derivative - d/dx	(d^43)/(dx^43)(sin(3x)+2^(5x))	$\frac{d^{43}}{d x^{43}} (\sin (3 x) + 2^{5 x})$
80575	Evaluate the Limit	limit as x approaches infinity of (5+x^-2)/(3x^-2+1)	$lim_{x \to \infty} \frac{5 + x^{- 2}}{3 x^{- 2} + 1}$
80576	Find the Maximum/Minimum Value	f(x)=-x^4+4x^2-3x-2	$f (x) = - x^{4} + 4 x^{2} - 3 x - 2$
80577	Evaluate the Limit	limit as x approaches 3 of (x^2-9)/(x-3)+ square root of x^2+5	$lim_{x \to 3} \frac{x^{2} - 9}{x - 3} + \sqrt{x^{2} + 5}$
80578	Evaluate the Integral	integral of 3xtan(5x^2-3) with respect to x	$\int 3 x \tan (5 x^{2} - 3) d x$
80579	Find Where Increasing/Decreasing	g(x)=x^5+x^4	$g (x) = x^{5} + x^{4}$
80580	Find the Antiderivative	(x^2)/( square root of x)	$\frac{x^{2}}{\sqrt{x}}$
80581	Evaluate the Integral	integral from 0 to 1 of arctan(4x) with respect to x	$\int_{0}^{1} \arctan (4 x) d x$
80582	Find the Antiderivative	f(x)=2 cube root of x-2/(x^4)+5x^3-8/( square root of x)-1	$f (x) = 2 \sqrt[3]{x} - \frac{2}{x^{4}} + 5 x^{3} - \frac{8}{\sqrt{x}} - 1$
80583	Find the Antiderivative	f(x)=6x-9+3x^5	$f (x) = 6 x - 9 + 3 x^{5}$
80584	Find Where Increasing/Decreasing	f(x)=-3/4x^4-x^3+108x^2+1	$f (x) = - \frac{3}{4} x^{4} - x^{3} + 108 x^{2} + 1$
80585	Find Where Increasing/Decreasing	y=8*(1/4)^x	$y = 8 \cdot {(\frac{1}{4})}^{x}$
80586	Evaluate the Integral	integral of 3x^2(2x-5)(3x-1) with respect to x	$\int 3 x^{2} (2 x - 5) (3 x - 1) d x$
80587	Integrate By Parts	integral of xsin(2x) with respect to x	$\int x \sin (2 x) d x$
80588	Determine if Continuous	f(x)=-3x+7 if x<=3; -2 if x>3	$f (x) = {\begin{cases} - 3 x + 7 & x \leq 3 \\ - 2 & x > 3 \end{cases}$
80589	Find the Antiderivative	arccos(x)	$\arccos (x)$
80590	Evaluate the Integral	integral of (4t^3-t^2+16t)/(t^2+4) with respect to t	$\int \frac{4 t^{3} - t^{2} + 16 t}{t^{2} + 4} d t$
80591	Find dy/dx	natural log of x^2+y^2+2arctan(x/y)=0	$\ln (x^{2} + y^{2}) + 2 \arctan (\frac{x}{y}) = 0$
80592	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(cos(2x))	$lim_{x \to 0} \frac{\sin (2 x)}{\cos (2 x)}$
80593	Find the Antiderivative	3x+8x^3+x^-3+5x^2	$3 x + 8 x^{3} + x^{- 3} + 5 x^{2}$
80594	Find the Derivative - d/dx	y = square root of 12x	$y = \sqrt{12 x}$
80595	Evaluate the Limit	limit as x approaches 8 of square root of (13-x)/(x+12)	$lim_{x \to 8} \sqrt{\frac{13 - x}{x + 12}}$
80596	Evaluate the Limit	limit as x approaches -6 of ((2x+8)/(x^2-12)-1/x)/(x+6)	$lim_{x \to - 6} \frac{\frac{2 x + 8}{x^{2} - 12} - \frac{1}{x}}{x + 6}$
80597	Find the Antiderivative	e^x+2x	$e^{x} + 2 x$
80598	Find the Antiderivative	1/x-1/(x^2)	$\frac{1}{x} - \frac{1}{x^{2}}$
80599	Evaluate the Integral	integral of (25x^4+x) with respect to x	$\int (25 x^{4} + x) d x$
80600	Integrate Using u-Substitution	integral of x square root of 2x+1 with respect to x	$\int x \sqrt{2 x + 1} d x$