Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
84501	Evaluate the Integral	integral of 1/(x square root of 4x^2+1) with respect to x	$\int \frac{1}{x \sqrt{4 x^{2} + 1}} d x$
84502	Find the Derivative - d/dx	d/(dx)cos(2x)	$\frac{d}{d x} \cos (2 x)$
84503	Find the Derivative - d/dx	(3-5x)/(2x^2-3)	$\frac{3 - 5 x}{2 x^{2} - 3}$
84504	Evaluate the Integral	integral from 1 to 4 of (x^2+x) with respect to x	$\int_{1}^{4} (x^{2} + x) d x$
84505	Evaluate the Limit	limit as x approaches negative infinity of (2x^2-7x^4)/(9x^2+5x-6)	$lim_{x \to - \infty} \frac{2 x^{2} - 7 x^{4}}{9 x^{2} + 5 x - 6}$
84506	Evaluate the Limit	limit as x approaches infinity of (x^2+5)/(x(2x^2+3))	$lim_{x \to \infty} \frac{x^{2} + 5}{x (2 x^{2} + 3)}$
84507	Find dy/dx	y = square root of x^2+2x	$y = \sqrt{x^{2} + 2 x}$
84508	Find the Maximum/Minimum Value	cos(x)	$\cos (x)$
84509	Find dz/dx	z = natural log of x^2+y^2	$z = \ln (x^{2} + y^{2})$
84510	Find the Second Derivative	3x^4-16x^3+24x^2+48	$3 x^{4} - 16 x^{3} + 24 x^{2} + 48$
84511	Find dy/dx	y = fifth root of x^2-8x+1	$y = \sqrt[5]{x^{2} - 8 x + 1}$
84512	Find the Antiderivative	x natural log of x+1	$x \ln (x + 1)$
84513	Evaluate from the Right	limit as x approaches 3 of 10/(x-2)	$lim_{x \to 3} \frac{10}{x - 2}$
84514	Find the Third Derivative	f(x)=4/3-1/2x^-1+1/4x^4+1/2x^3	$f (x) = \frac{4}{3} - \frac{1}{2} x^{- 1} + \frac{1}{4} x^{4} + \frac{1}{2} x^{3}$
84515	Find the Derivative - d/dx	(1- natural log of x)/(x^2)	$\frac{(1 - \ln (x))}{x^{2}}$
84516	Find the Derivative - d/dx	square root of 4/x- square root of 3x	$\sqrt{\frac{4}{x}} - \sqrt{3 x}$
84517	Integrate Using u-Substitution	integral of 1/((1-6t)^4) with respect to t	$\int \frac{1}{{(1 - 6 t)}^{4}} d t$
84518	Find the Derivative - d/dx	y=(e^( natural log of x))^2	$y = {(e^{\ln (x)})}^{2}$
84519	Evaluate the Summation	sum from k=0 to 6 of -k^2-9	$\sum_{k = 0}^{6} - k^{2} - 9$
84520	Evaluate the Integral	integral from -7 to 0 of (y/7+ square root of y+8) with respect to y	$\int_{- 7}^{0} (\frac{y}{7} + \sqrt{y + 8}) d y$
84521	Find the Derivative - d/dx	d/(dx)x^5y^10-x^3sin(z)+y^2e^z	$\frac{d}{d x} x^{5} y^{10} - x^{3} \sin (z) + y^{2} e^{z}$
84522	Find dy/dx	y=(6 cube root of x)/5	$y = \frac{6 \sqrt[3]{x}}{5}$
84523	Find the Tangent Line at (2,16)	f(x)=2x^3 at (2,16)	$f (x) = 2 x^{3}$ at $(2, 16)$
84524	Evaluate the Limit	limit as x approaches infinity of ( square root of 6x+5x^2)/(6x-1)	$lim_{x \to \infty} \frac{\sqrt{6 x + 5 x^{2}}}{6 x - 1}$
84525	Evaluate the Integral	integral of (sec(x)tan(x))/(sec(x)-1) with respect to x	$\int \frac{\sec (x) \tan (x)}{\sec (x) - 1} d x$
84526	Find the Derivative - d/dx	2x-27x^-2	$2 x - 27 x^{- 2}$
84527	Evaluate the Integral	integral from 0 to infinity of e^(-st) with respect to t	$\int_{0}^{\infty} e^{- s t} d t$
84528	Find the Antiderivative	(1/2x-1)^7	${(\frac{1}{2} x - 1)}^{7}$
84529	Evaluate the Limit	limit as x approaches 0 of (8e^x-8)/x	$lim_{x \to 0} \frac{8 e^{x} - 8}{x}$
84530	Evaluate the Limit	limit as x approaches infinity of (1+5e^x)^(1/x)	$lim_{x \to \infty} {(1 + 5 e^{x})}^{\frac{1}{x}}$
84531	Find the Antiderivative	f(x)=2sin(6x+3)-4x	$f (x) = 2 \sin (6 x + 3) - 4 x$
84532	Evaluate the Limit	limit as a approaches 2 of (a^2-4a+4)/(a^2-4)	$lim_{a \to 2} \frac{a^{2} - 4 a + 4}{a^{2} - 4}$
84533	Evaluate the Integral	integral of 1/(theta^2)sin(1/theta)cos(1/theta) with respect to theta	$\int \frac{1}{θ^{2}} \sin (\frac{1}{θ}) \cos (\frac{1}{θ}) d θ$
84534	Find dy/dx	3x^2+24x-y^2+2y=-44	$3 x^{2} + 24 x - y^{2} + 2 y = - 44$
84535	Evaluate the Summation	4 sum from t=0 to 3 of -2t+4t^2	$4 \sum_{t = 0}^{3} - 2 t + 4 t^{2}$
84536	Find the Fourth Derivative	256/2401	$\frac{256}{2401}$
84537	Find the Derivative - d/dx	2/x+1/(4x^2)	$\frac{2}{x} + \frac{1}{4 x^{2}}$
84538	Solve the Differential Equation	y'=y^2	$y' = y^{2}$
84539	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 7+4x^2)/(2x+5)	$lim_{x \to - \infty} \frac{\sqrt{7 + 4 x^{2}}}{2 x + 5}$
84540	Find the Third Derivative	f(x)=-1/4x^5+1/20x^6+1/4x^-3+1/2x^3	$f (x) = - \frac{1}{4} x^{5} + \frac{1}{20} x^{6} + \frac{1}{4} x^{- 3} + \frac{1}{2} x^{3}$
84541	Evaluate the Integral	integral from 0 to 2 of (4x^3-3x^2+2x) with respect to x	$\int_{0}^{2} (4 x^{3} - 3 x^{2} + 2 x) d x$
84542	Find the Antiderivative	(x+1)^-2	${(x + 1)}^{- 2}$
84543	Evaluate the Integral	integral from 1 to e of ( square root of natural log of x)/x with respect to x	$\int_{1}^{e} \frac{\sqrt{\ln (x)}}{x} d x$
84544	Find the Derivative - d/dx	4x^2-1/x	$4 x^{2} - \frac{1}{x}$
84545	Find the Antiderivative	f(x)=4e^(-2x)+(x-1)^3	$f (x) = 4 e^{- 2 x} + {(x - 1)}^{3}$
84546	Find the Derivative - d/dx	\|x^2-4x\|	$\| x^{2} - 4 x \|$
84547	Evaluate from the Left	limit as x approaches 2 of x+3	$lim_{x \to 2} x + 3$
84548	Evaluate the Limit	limit as x approaches 1 of natural log of 3x^2+4	$lim_{x \to 1} \ln (3 x^{2} + 4)$
84549	Integrate Using Trig Substitution	integral from 0 to 3 of x/( square root of 36-x^2) with respect to x	$\int_{0}^{3} \frac{x}{\sqrt{36 - x^{2}}} d x$
84550	Find the Derivative - d/dx	cot(x)csc(x)	$\cot (x) \csc (x)$
84551	Find the Maximum/Minimum Value	f(x)=-x^4-7x^3-12x^2	$f (x) = - x^{4} - 7 x^{3} - 12 x^{2}$
84552	Integrate Using u-Substitution	integral of x^3 square root of 1+x^2 with respect to x	$\int x^{3} \sqrt{1 + x^{2}} d x$
84553	Evaluate the Integral	integral from 0 to pi/4 of 1/(cos(x)^2) with respect to x	$\int_{0}^{\frac{π}{4}} \frac{1}{\cos^{2} (x)} d x$
84554	Evaluate from the Left	limit as x approaches 0 of square root of x	$lim_{x \to 0} \sqrt{x}$
84555	Find the Maximum/Minimum Value	f(x)=-\|x\|+7	$f (x) = - \| x \| + 7$
84556	Evaluate the Integral	integral of (4e^2)/(x^-3) with respect to x	$\int \frac{4 e^{2}}{x^{- 3}} d x$
84557	Find dy/dx	sin(xy)=y	$\sin (x y) = y$
84558	Find the Derivative - d/dy	1/(e^y)	$\frac{1}{e^{y}}$
84559	Find the Derivative - d/dx	x^3-3x^2y+3xy^2-y^3	$x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}$
84560	Evaluate the Integral	integral of ((3x^2+4x+1)/(2x)) with respect to x	$\int (\frac{3 x^{2} + 4 x + 1}{2 x}) d x$
84561	Find the Derivative - d/dx	d/(dx)e^(-x^2)	$\frac{d}{d x} e^{- x^{2}}$
84562	Find the Integral	1-x	$1 - x$
84563	Find the Antiderivative	f(x)=x-9x^2+4	$f (x) = x - 9 x^{2} + 4$
84564	Find the Derivative - d/dx	sin(x^3-2x)	$\sin (x^{3} - 2 x)$
84565	Evaluate the Integral	integral of (x^4-3x^(5/2)+ square root of x+2) with respect to x	$\int (x^{4} - 3 x^{\frac{5}{2}} + \sqrt{x} + 2) d x$
84566	Find the Derivative - d/dx	x natural log of x^2+4x	$x \ln (x^{2} + 4 x)$
84567	Find the Center and Radius	x^2+Y^2+2X-4Y=0	$x^{2} + Y^{2} + 2 X - 4 Y = 0$
84568	Evaluate the Integral	integral of (tan(11 square root of x))/( square root of x) with respect to x	$\int \frac{\tan (11 \sqrt{x})}{\sqrt{x}} d x$
84569	Find the Derivative of the Integral	integral from 0 to natural log of x of 1/( square root of 4+e^t) with respect to t	$\int_{0}^{\ln (x)} \frac{1}{\sqrt{4 + e^{t}}} d t$
84570	Evaluate the Limit	limit as x approaches 0 of (7e^x-7)/x	$lim_{x \to 0} \frac{7 e^{x} - 7}{x}$
84571	Evaluate the Summation	sum from i=1 to 3 of x_i	$\sum_{i = 1}^{3} x_{i}$
84572	Find the Derivative - d/dx	-( cube root of x^4)/6	$- \frac{\sqrt[3]{x^{4}}}{6}$
84573	Integrate Using u-Substitution	integral of sin(4x)cos(4x) with respect to x	$\int \sin (4 x) \cos (4 x) d x$
84574	Determine if Continuous	f(x)=(x^2-x-12)/(x-4),x!=4; 7,x=4	$f (x) = {\begin{cases} \frac{x^{2} - x - 12}{x - 4}, x \neq 4 \\ 7, x = 4 \end{cases}$
84575	Evaluate the Limit	limit as x approaches pi/2 of (1/(cos(x)))^2	$lim_{x \to \frac{π}{2}} {(\frac{1}{\cos (x)})}^{2}$
84576	Find the Derivative - d/dx	y=tan(x)+1/3tan(x)^3	$y = \tan (x) + \frac{1}{3} \tan^{3} (x)$
84577	Find the Derivative - d/dx	sin(x)x^2	$\sin (x) x^{2}$
84578	Find the Derivative - d/dx	xe^y+ye^x	$x e^{y} + y e^{x}$
84579	Evaluate the Integral	integral of 5tan(3x) natural log of sec(3x) with respect to x	$\int 5 \tan (3 x) \ln (\sec (3 x)) d x$
84580	Find the Upper and Lower Bounds	F(x)=2x^3+3x^2-13x-15	$F (x) = 2 x^{3} + 3 x^{2} - 13 x - 15$
84581	Evaluate the Integral	integral of 8(4x^2-5)^9x with respect to x	$\int 8 {(4 x^{2} - 5)}^{9} x d x$
84582	Find the Inflection Points	-1/3x^3-9x^2	$- \frac{1}{3} x^{3} - 9 x^{2}$
84583	Find the Derivative - d/dx	y=(-x^2+e^x)(2sin(x)+cos(x))	$y = (- x^{2} + e^{x}) (2 \sin (x) + \cos (x))$
84584	Evaluate the Integral	integral of -4/( square root of 16-36x^2) with respect to x	$\int \frac{- 4}{\sqrt{16 - 36 x^{2}}} d x$
84585	Find the Derivative - d/dx	(1-sin(x))^(-1/2)	${(1 - \sin (x))}^{- \frac{1}{2}}$
84586	Evaluate the Integral	integral of 9/(2(9-2x)^(1/4)) with respect to x	$\int \frac{9}{2 {(9 - 2 x)}^{\frac{1}{4}}} d x$
84587	Find the Derivative - d/dx	square root of (x^2-3x)/(2x+1)	$\sqrt{\frac{x^{2} - 3 x}{2 x + 1}}$
84588	Find dy/dx	y=3sin(2x^3)^2	$y = 3 \sin^{2} (2 x^{3})$
84589	Find the Antiderivative	(x+1)/(2x+3)	$\frac{x + 1}{2 x + 3}$
84590	Evaluate the Integral	integral of (1+3x^2-5x^3) with respect to x	$\int (1 + 3 x^{2} - 5 x^{3}) d x$
84591	Evaluate the Integral	integral of (4+e^x)^-4e^x with respect to x	$\int {(4 + e^{x})}^{- 4} e^{x} d x$
84592	Find the Antiderivative	4/( square root of x)+3/x-2e^(-x)	$\frac{4}{\sqrt{x}} + \frac{3}{x} - 2 e^{- x}$
84593	Evaluate the Integral	integral of (-5x^-2+x) with respect to x	$\int (- 5 x^{- 2} + x) d x$
84594	Find the Derivative - d/dθ	y=cos(theta)cot(theta)	$y = \cos (θ) \cot (θ)$
84595	Find the Antiderivative	( square root of x)^2	${(\sqrt{x})}^{2}$
84596	Evaluate the Integral	integral of 1+(sin(x)-cos(x))^2 with respect to x	$\int 1 + {(\sin (x) - \cos (x))}^{2} d x$
84597	Evaluate the Integral	integral of (2x^3)/(x^2-4) with respect to x	$\int \frac{2 x^{3}}{x^{2} - 4} d x$
84598	Evaluate the Integral	integral from 0 to cube root of pi of x^2cos(x^3) with respect to x	$\int_{0}^{\sqrt[3]{π}} x^{2} \cos (x^{3}) d x$
84599	Find the Antiderivative	(sin(x))/(cos(x))	$\frac{(\sin (x))}{\cos (x)}$
84600	Find the Antiderivative	(3x^2+5x-1)/(x-2)	$\frac{3 x^{2} + 5 x - 1}{x - 2}$