Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
82301	Find dy/dx	-y^3+5-y^2+y=2x^3	$- y^{3} + 5 - y^{2} + y = 2 x^{3}$
82302	Find the Antiderivative	(cos(x))/((2+sin(x))^2)	$\frac{\cos (x)}{{(2 + \sin (x))}^{2}}$
82303	Find the Antiderivative	f(x)=3/(x^2)-2/(x^3)	$f (x) = \frac{3}{x^{2}} - \frac{2}{x^{3}}$
82304	Find dy/dx	-x^3=3y-y^2	$- x^{3} = 3 y - y^{2}$
82305	Find dy/dx	-xy-4y^2+x-4=0	$- x y - 4 y^{2} + x - 4 = 0$
82306	Find dy/dx	y-2y^2=-x^3-y^3	$y - 2 y^{2} = - x^{3} - y^{3}$
82307	Find the Derivative of the Integral	F(x) = integral from x to 0 of square root of t^2+1 with respect to t	$F (x) = \int_{x}^{0} \sqrt{t^{2} + 1} d t$
82308	Find the Integral	(dx)/(1+x^2)	$\frac{d x}{1 + x^{2}}$
82309	Find dy/dx	e^(xy)=y-x	$e^{x y} = y - x$
82310	Find the Derivative - d/dx	y=cos(x^2)*sin(x^2)	$y = \cos (x^{2}) \cdot \sin (x^{2})$
82311	Evaluate the Limit	limit as x approaches 0 of e^(-x)	$lim_{x \to 0} e^{- x}$
82312	Evaluate the Integral	integral from -1 to 1 of 3\|x^3\| with respect to x	$\int_{- 1}^{1} 3 \| x^{3} \| d x$
82313	Evaluate the Integral	integral of (1/(x^3)-1/(x^2)) with respect to x	$\int (\frac{1}{x^{3}} - \frac{1}{x^{2}}) d x$
82314	Evaluate Using Summation Formulas	sum from i=1 to 9 of 3i^2+8i-5	$\sum_{i = 1}^{9} 3 i^{2} + 8 i - 5$
82315	Evaluate the Limit	limit as x approaches 0 of (2xcos(8x)+2sin(5x))/(tan(2x))	$lim_{x \to 0} \frac{2 x \cos (8 x) + 2 \sin (5 x)}{\tan (2 x)}$
82316	Find the Antiderivative	1/(x^3)+2	$\frac{1}{x^{3}} + 2$
82317	Find the Derivative - d/dx	1/(2 cube root of x^5)	$\frac{1}{2 \sqrt[3]{x^{5}}}$
82318	Evaluate the Integral	integral of 3e^(3-7x) with respect to x	$\int 3 e^{3 - 7 x} d x$
82319	Find dy/dx	-4+x^3=x^3y-y^3	$- 4 + x^{3} = x^{3} y - y^{3}$
82320	Find the Antiderivative	f(x)=x^3-2/( square root of x)	$f (x) = x^{3} - \frac{2}{\sqrt{x}}$
82321	Find Where Increasing/Decreasing	f(x)=5/x+3x	$f (x) = \frac{5}{x} + 3 x$
82322	Find the Derivative - d/dx	d/(dx)(-sin(x))	$\frac{d}{d x} (- \sin (x))$
82323	Evaluate the Integral	integral from 0 to 0.5 of x(1-x)^3 with respect to x	$\int_{0}^{0.5} x {(1 - x)}^{3} d x$
82324	Find dy/dx	5y^2-3-x^3=0	$5 y^{2} - 3 - x^{3} = 0$
82325	Find the Second Derivative	-2/5x^6+5x^4	$- \frac{2}{5} x^{6} + 5 x^{4}$
82326	Evaluate the Integral	integral of (( square root of x)/2+2/( square root of x)) with respect to x	$\int (\frac{\sqrt{x}}{2} + \frac{2}{\sqrt{x}}) d x$
82327	Find the Derivative - d/dr	v=1/3pir^2h	$v = \frac{1}{3} π r^{2} h$
82328	Evaluate the Limit	limit as x approaches 0 of 3xcsc(2x)	$lim_{x \to 0} 3 x \csc (2 x)$
82329	Find dy/dx	-1+x^3-5y^3=-y^2	$- 1 + x^{3} - 5 y^{3} = - y^{2}$
82330	Find the Derivative - d/dx	(4x^2-3)^2(x+5)^3	${(4 x^{2} - 3)}^{2} {(x + 5)}^{3}$
82331	Find dy/dx	-xy+2y+5x^2=-4	$- x y + 2 y + 5 x^{2} = - 4$
82332	Integrate Using u-Substitution	integral of x^3 square root of x^2+4 with respect to x	$\int x^{3} \sqrt{x^{2} + 4} d x$
82333	Find dy/dx	3x^3-5-2y^3=xy	$3 x^{3} - 5 - 2 y^{3} = x y$
82334	Eliminate the Parameter	x=2t-5 , y=t^2+4	$x = 2 t - 5$ , $y = t^{2} + 4$
82335	Evaluate the Integral	integral of (x-2)/(2x^2) with respect to x	$\int \frac{x - 2}{2 x^{2}} d x$
82336	Find the Inflection Points	1/10x^5-12x^3	$\frac{1}{10} x^{5} - 12 x^{3}$
82337	Evaluate the Integral	integral from negative infinity to 3 of 1/((x-3)^3) with respect to x	$\int_{- \infty}^{3} \frac{1}{{(x - 3)}^{3}} d x$
82338	Evaluate from the Right	limit as x approaches -1 of x^2+1	$lim_{x \to - 1} x^{2} + 1$
82339	Find the Critical Points	f(x)=x/( square root of x^2+1)	$f (x) = \frac{x}{\sqrt{x^{2} + 1}}$
82340	Find the Integral	1/(x(x+1))	$\frac{1}{x (x + 1)}$
82341	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of x^(1/(x^2))	$lim_{x \to \infty} x^{\frac{1}{x^{2}}}$
82342	Integrate Using u-Substitution	integral of e^( square root of x) with respect to x	$\int e^{\sqrt{x}} d x$
82343	Find the Antiderivative	f(x)=5cos(4x-2)+5x	$f (x) = 5 \cos (4 x - 2) + 5 x$
82344	Evaluate the Limit	limit as x approaches 0 from the right of sin(x)^x	$lim_{x \to 0^{+}} {\sin (x)}^{x}$
82345	Find Where Increasing/Decreasing	f(x) = square root of x+5	$f (x) = \sqrt{x} + 5$
82346	Find the Maximum/Minimum Value	y=x+1/(9x)	$y = x + \frac{1}{9 x}$
82347	Find the Concavity	3/5x^5-x^4-12x^3	$\frac{3}{5} x^{5} - x^{4} - 12 x^{3}$
82348	Find dy/dx	x^2-x^3=-2y^2	$x^{2} - x^{3} = - 2 y^{2}$
82349	Evaluate the Integral	integral of (x^4+4)^(1/2)x^3 with respect to x	$\int {(x^{4} + 4)}^{\frac{1}{2}} x^{3} d x$
82350	Evaluate the Integral	integral of (t^2-sin(t)) with respect to t	$\int (t^{2} - \sin (t)) d t$
82351	Evaluate the Limit	limit as h approaches 0 of (15((h-8)^2-64))/h	$lim_{h \to 0} \frac{15 ({(h - 8)}^{2} - 64)}{h}$
82352	Find the Domain and Range	f(x)=1 if x<-5; -x if -5<=x<=3; \|x-4\|-7 if x>3	$f (x) = {\begin{cases} 1 & x < - 5 \\ - x & - 5 \leq x \leq 3 \\ \| x - 4 \| - 7 & x > 3 \end{cases}$
82353	Find the Derivative - d/dx	( log base 5 of x)/(x^2)	$\frac{\log_{5} (x)}{x^{2}}$
82354	Find dy/dx	x^3+2x^2y-4y=7	$x^{3} + 2 x^{2} y - 4 y = 7$
82355	Evaluate the Limit	limit as x approaches c of infinity+-2	$lim_{x \to c} \infty + - 2$
82356	Find the Integral	(-9x^2+10x)dx ?	$(- 9 x^{2} + 10 x) d x$ ?
82357	Evaluate the Limit	limit as x approaches 5 of 3^(x+1)	$lim_{x \to 5} 3^{x + 1}$
82358	Evaluate the Integral	integral from -5 to 5 of e with respect to x	$\int_{- 5}^{5} e d x$
82359	Integrate By Parts	integral of 5x^6 natural log of 2x with respect to x	$\int 5 x^{6} \ln (2 x) d x$
82360	Find the Derivative - d/dx	(\|x\|)/x	$\frac{\| x \|}{x}$
82361	Evaluate the Limit	limit as x approaches -b of ((x+b)^7+(x+b)^10)/(4(x+b))	$lim_{x \to - b} \frac{{(x + b)}^{7} + {(x + b)}^{10}}{4 (x + b)}$
82362	Find the Derivative - d/dx	1/(e^x+1)	$\frac{1}{e^{x} + 1}$
82363	Evaluate the Limit	limit as x approaches infinity of (x^3)/(e^x)	$lim_{x \to \infty} \frac{x^{3}}{e^{x}}$
82364	Evaluate the Summation	sum from n=2 to 5 of x-n	$\sum_{n = 2}^{5} x - n$
82365	Evaluate the Limit	limit as x approaches negative infinity of (2x^4-8x+x+2)/(4x^4-5x^2-2)	$lim_{x \to - \infty} \frac{2 x^{4} - 8 x + x + 2}{4 x^{4} - 5 x^{2} - 2}$
82366	Evaluate the Limit	limit as x approaches 6 of (2x-1) square root of x+4	$lim_{x \to 6} (2 x - 1) \sqrt{x + 4}$
82367	Evaluate Using L'Hospital's Rule	limit as x approaches -1 of (2+2x)/(e^(-2-2x)+x^3)	$lim_{x \to - 1} \frac{2 + 2 x}{e^{- 2 - 2 x} + x^{3}}$
82368	Find the Antiderivative	y=1/x	$y = \frac{1}{x}$
82369	Find the Second Derivative	y=3x^(2/3)-2x	$y = 3 x^{\frac{2}{3}} - 2 x$
82370	Find the Derivative of the Integral	integral of (x+1)(x+a) with respect to x	$\int (x + 1) (x + a) d x$
82371	Find the Derivative - d/dx	(arcsin(e^(5x)))	$(\arcsin (e^{5 x}))$
82372	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (3e^x-3)/( natural log of 1-x-x^3)	$lim_{x \to 0} \frac{3 e^{x} - 3}{\ln (1 - x) - x^{3}}$
82373	Evaluate the Limit	limit as x approaches 8 of (x^2+1)(x^(2/3))	$lim_{x \to 8} (x^{2} + 1) (x^{\frac{2}{3}})$
82374	Evaluate the Integral	integral of ((x^2-1)^3)/(x^2) with respect to x	$\int \frac{{(x^{2} - 1)}^{3}}{x^{2}} d x$
82375	Evaluate the Integral	integral from 0 to 5 of pi((20-4x)/5)^2 with respect to x	$\int_{0}^{5} π {(\frac{20 - 4 x}{5})}^{2} d x$
82376	Evaluate the Limit	limit as x approaches 8 of 2f(x)-12h(x)	$lim_{x \to 8} 2 f (x) - 12 h (x)$
82377	Find the Derivative - d/dx	d/(dx)( log base 7 of 1-x)	$\frac{d}{d x} (\log_{7} (1 - x))$
82378	Evaluate the Integral	integral of (5 cube root of x^4)/3 with respect to x	$\int \frac{5 \sqrt[3]{x^{4}}}{3} d x$
82379	Find the Antiderivative	((x-1)^3)/(2x^2)	$\frac{{(x - 1)}^{3}}{2 x^{2}}$
82380	Find the Maximum/Minimum Value	y=-2cos(x)+5	$y = - 2 \cos (x) + 5$
82381	Find dy/dx	y=x^2-xcos(x)	$y = x^{2} - x \cos (x)$
82382	Find the Antiderivative	x*e^(-x^2)	$x \cdot e^{- x^{2}}$
82383	Find dy/dx	5+3xy+4y^3=0	$5 + 3 x y + 4 y^{3} = 0$
82384	Evaluate the Limit	limit as x approaches infinity of 3-7/x+4/(x^2)	$lim_{x \to \infty} 3 - \frac{7}{x} + \frac{4}{x^{2}}$
82385	Find dy/dx	3y^2=x^2+2x^3-y^3	$3 y^{2} = x^{2} + 2 x^{3} - y^{3}$
82386	Find dy/dx	-3+xy-y^2=2x^2	$- 3 + x y - y^{2} = 2 x^{2}$
82387	Find dy/dx	-y^2-xy-2x=0	$- y^{2} - x y - 2 x = 0$
82388	Find the Antiderivative	xe^(x^2+1)	$x e^{x^{2} + 1}$
82389	Evaluate the Integral	integral from 0 to 1 of (x^15+15^x) with respect to x	$\int_{0}^{1} (x^{15} + 15^{x}) d x$
82390	Find Where Increasing/Decreasing	f(x)=3+2x-x^2	$f (x) = 3 + 2 x - x^{2}$
82391	Find the Antiderivative	3x^2+x/2	$3 x^{2} + \frac{x}{2}$
82392	Integrate Using u-Substitution	integral of cot(x)^2 with respect to x	$\int \cot^{2} (x) d x$
82393	Find Where Increasing/Decreasing	h(x)=x^4-3x^2+x	$h (x) = x^{4} - 3 x^{2} + x$
82394	Find dy/dx	-5x^2+y^2-x^3=-x	$- 5 x^{2} + y^{2} - x^{3} = - x$
82395	Evaluate the Integral	integral from 0 to pi of 4/(x^2+1) with respect to x	$\int_{0}^{π} \frac{4}{x^{2} + 1} d x$
82396	Evaluate the Integral	integral of (7csc(x)^2+2sec(x)tan(x)) with respect to x	$\int (7 \csc^{2} (x) + 2 \sec (x) \tan (x)) d x$
82397	Find the Derivative - d/dx	\|x^2\|	$\| x^{2} \|$
82398	Find dy/dx	-2y+5x^2-5y^2=-4	$- 2 y + 5 x^{2} - 5 y^{2} = - 4$
82399	Find the Antiderivative	x*(x^2+7)^15	$x \cdot {(x^{2} + 7)}^{15}$
82400	Find the Skew	1 , 2 , 4 , 7 , 9 , 10	$1$ , $2$ , $4$ , $7$ , $9$ , $10$