Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
81701	Find the Antiderivative	(x^2)/x	$\frac{x^{2}}{x}$
81702	Find the Derivative - d/dx	\|2x+1\|	$\| 2 x + 1 \|$
81703	Find Where Increasing/Decreasing	((x+1)^2)/(x-4)	$\frac{{(x + 1)}^{2}}{x - 4}$
81704	Find the Concavity	f(x)=-1/15x^6-x^5	$f (x) = - \frac{1}{15} x^{6} - x^{5}$
81705	Find the Maximum/Minimum Value	f(x)=x^4-4x^3+2x^2+4x-3	$f (x) = x^{4} - 4 x^{3} + 2 x^{2} + 4 x - 3$
81706	Solve the Differential Equation	y'=(y^2+x^2)/(2xy)	$y' = \frac{y^{2} + x^{2}}{2 x y}$
81707	Find dy/dx	x^2+y^3=-2+y^2	$x^{2} + y^{3} = - 2 + y^{2}$
81708	Find the Derivative - d/dx	2cos(x)+cos(2x)	$2 \cos (x) + \cos (2 x)$
81709	Evaluate the Integral	integral of (3sec(6x)tan(6x)-5xcsc(2x^2)^2) with respect to x	$\int (3 \sec (6 x) \tan (6 x) - 5 x \csc^{2} (2 x^{2})) d x$
81710	Evaluate the Integral	integral of (x^2-3x+5)e^x with respect to x	$\int (x^{2} - 3 x + 5) e^{x} d x$
81711	Find the Derivative - d/dx	y=(12e^(6x)-9e^(8x))/(3e^(3x))	$y = \frac{12 e^{6 x} - 9 e^{8 x}}{3 e^{3 x}}$
81712	Find the Maximum/Minimum Value	f(x)=-x(x+2)(x-2)	$f (x) = - x (x + 2) (x - 2)$
81713	Evaluate the Integral	integral from 1 to 2 of (-4x^(3/2)+2 square root of x-4x^3) with respect to x	$\int_{1}^{2} (- 4 x^{\frac{3}{2}} + 2 \sqrt{x} - 4 x^{3}) d x$
81714	Integrate Using u-Substitution	integral from 1 to 2 of (e^(1/x))/(x^2) with respect to x	$\int_{1}^{2} \frac{e^{\frac{1}{x}}}{x^{2}} d x$
81715	Find the Derivative - d/dx	1/x+e^x	$\frac{1}{x} + e^{x}$
81716	Evaluate the Limit	limit as t approaches -2 of t^3(4-6t^2)	$lim_{t \to - 2} t^{3} (4 - 6 t^{2})$
81717	Find the Antiderivative	(dx)/( square root of x)	$\frac{d x}{\sqrt{x}}$
81718	Find the Antiderivative	1+cos(x)^2	$1 + \cos^{2} (x)$
81719	Find dy/dx	2x^3=y-y^2	$2 x^{3} = y - y^{2}$
81720	Find the Derivative - d/dx	2^(2x+3)	$2^{2 x + 3}$
81721	Find dy/dx	x+cos(x+y)=0	$x + \cos (x + y) = 0$
81722	Find the Derivative - d/dx	2x^4(3x^2+7x)	$2 x^{4} (3 x^{2} + 7 x)$
81723	Integrate Using u-Substitution	integral from 1 to 2 of x square root of x-1 with respect to x	$\int_{1}^{2} x \sqrt{x - 1} d x$
81724	Evaluate the Limit	limit as x approaches 2 of (2x-x^2)/(x^2-4)	$lim_{x \to 2} \frac{2 x - x^{2}}{x^{2} - 4}$
81725	Find the Derivative - d/dx	g (x)=3sin( cube root of x)	$g$ $(x) = 3 \sin (\sqrt[3]{x})$
81726	Find the Percentage Rate of Change	p(t)=1.8^t	$p (t) = {1.8}^{t}$
81727	Evaluate the Limit	limit as x approaches 2 of ( square root of x+7-3)/(2-x)	$lim_{x \to 2} \frac{\sqrt{x + 7} - 3}{2 - x}$
81728	Evaluate the Integral	integral of (2x^4-6x^5+3x^-3) with respect to x	$\int (2 x^{4} - 6 x^{5} + 3 x^{- 3}) d x$
81729	Find the Derivative - d/dx	-1/(4(x+1)^(3/2))	$- \frac{1}{4 {(x + 1)}^{\frac{3}{2}}}$
81730	Evaluate the Limit	limit as x approaches 0 of (2x^2-3x+4)/x+(5x-4)/x	$lim_{x \to 0} \frac{2 x^{2} - 3 x + 4}{x} + \frac{5 x - 4}{x}$
81731	Evaluate the Integral	integral from 0 to pi/2 of x^2sin(x) with respect to x	$\int_{0}^{\frac{π}{2}} x^{2} \sin (x) d x$
81732	Find the Derivative - d/dx	y=(cos(mx))/(sin(nx))	$y = \frac{\cos (m x)}{\sin (n x)}$
81733	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 9x^2-4)/(3x+5)	$lim_{x \to - \infty} \frac{\sqrt{9 x^{2} - 4}}{3 x + 5}$
81734	Find the Maximum/Minimum Value	f(x)=-x^4+x^3+19	$f (x) = - x^{4} + x^{3} + 19$
81735	Integrate By Parts	integral of natural log of 5x with respect to x	$\int \ln (5 x) d x$
81736	Find the Inflection Points	-1/6x^6-2x^5	$- \frac{1}{6} x^{6} - 2 x^{5}$
81737	Evaluate the Limit	limit as x approaches 4 of (f(x)-5)/(x-2)=1	$lim_{x \to 4} \frac{f (x) - 5}{x - 2} = 1$
81738	Find the Integral	2xe^x	$2 x e^{x}$
81739	Find the Derivative - d/dx	y=csc(2x)^4	$y = \csc^{4} (2 x)$
81740	Find the Derivative - d/dx	(cos(x/2))/2	$\frac{\cos (\frac{x}{2})}{2}$
81741	Find dy/dx	5x^3-x^2+3y=2+4y^2	$5 x^{3} - x^{2} + 3 y = 2 + 4 y^{2}$
81742	Evaluate the Limit	limit as x approaches -1 of (x^2+11x+10)/(x^2+x)	$lim_{x \to - 1} \frac{x^{2} + 11 x + 10}{x^{2} + x}$
81743	Find the Derivative - d/dx	d/(dx)(3cos(x^2+5))	$\frac{d}{d x} (3 \cos (x^{2} + 5))$
81744	Find the Derivative - d/dx	y=(3x^2-6x+1)^2	$y = {(3 x^{2} - 6 x + 1)}^{2}$
81745	Find dy/dx	3y^3+4x^3+5y^2+5y+2x=0	$3 y^{3} + 4 x^{3} + 5 y^{2} + 5 y + 2 x = 0$
81746	Find the Antiderivative	1/( square root of x)-2/( cube root of x)	$\frac{1}{\sqrt{x}} - \frac{2}{\sqrt[3]{x}}$
81747	Evaluate the Integral	integral of 2x^2(2x+1)(x-3) with respect to x	$\int 2 x^{2} (2 x + 1) (x - 3) d x$
81748	Determine if Continuous	f(x)=(x^2-x-2)/(x-2),x!=2; 3,x=2	$f (x) = {\begin{cases} \frac{x^{2} - x - 2}{x - 2}, x \neq 2 \\ 3, x = 2 \end{cases}$
81749	Find dy/dx	(x^3+2y^2)^5=y	${(x^{3} + 2 y^{2})}^{5} = y$
81750	Find the Derivative - d/dy	(x^2)/(2y)+(3y^2)/x	$\frac{x^{2}}{2 y} + \frac{3 y^{2}}{x}$
81751	Evaluate the Limit	limit as x approaches -2 of 1/(\|x\|)	$lim_{x \to - 2} \frac{1}{\| x \|}$
81752	Evaluate the Integral	integral from negative infinity to infinity of x/( square root of x^2+9) with respect to x	$\int_{- \infty}^{\infty} \frac{x}{\sqrt{x^{2} + 9}} d x$
81753	Find Where Increasing/Decreasing	(e^x)/(x^2)	$\frac{e^{x}}{x^{2}}$
81754	Find the Derivative - d/dx	-1/2cos(2x)	$- \frac{1}{2} \cos (2 x)$
81755	Find the Derivative - d/dx	x square root of 3-2x	$x \sqrt{3 - 2 x}$
81756	Evaluate the Limit	limit as x approaches -4 of (3(x+1)^2-27)/(x+4)	$lim_{x \to - 4} \frac{3 {(x + 1)}^{2} - 27}{x + 4}$
81757	Find the Maximum/Minimum Value	e^x+e^(-x)	$e^{x} + e^{- x}$
81758	Find dy/dx	y square root of y^3+1=x	$y \sqrt{y^{3} + 1} = x$
81759	Evaluate the Integral	integral from 0 to 1 of x^3e^(-x^4) with respect to x	$\int_{0}^{1} x^{3} e^{- x^{4}} d x$
81760	Evaluate the Integral	integral from 0 to 1 of x/( square root of 4-4x^2) with respect to x	$\int_{0}^{1} \frac{x}{\sqrt{4 - 4 x^{2}}} d x$
81761	Evaluate the Integral	integral from 2 to infinity of 5/((x+2)( natural log of x+2)^2) with respect to x	$\int_{2}^{\infty} \frac{5}{(x + 2) \ln^{2} (x + 2)} d x$
81762	Find the Antiderivative	1/(x* natural log of x)	$\frac{1}{x \cdot \ln (x)}$
81763	Evaluate the Integral	integral from 0 to k of (2kx-x^2) with respect to x=18	$\int_{0}^{k} (2 k x - x^{2}) d x = 18$
81764	Evaluate the Limit	limit as x approaches 1 of cos(x/3)	$lim_{x \to 1} \cos (\frac{x}{3})$
81765	Find the Tangent Line at (1/2,32)	f(t)=t^-5 ;, (1/2,32)	$f (t) = t^{- 5}$ ;, $(\frac{1}{2}, 32)$
81766	Evaluate the Summation	sum from i=7 to 23 of 2x+1	$\sum_{i = 7}^{23} 2 x + 1$
81767	Evaluate the Integral	integral from -2 to 1 of (x^4+x^3-4x^2+6) with respect to x	$\int_{- 2}^{1} (x^{4} + x^{3} - 4 x^{2} + 6) d x$
81768	Find the Antiderivative	(dx)/(1+x^2)	$\frac{d x}{1 + x^{2}}$
81769	Find the Derivative - d/dx	(x-1)^2sin(x)	${(x - 1)}^{2} \sin (x)$
81770	Find the Antiderivative	(1+ natural log of x)/x	$\frac{1 + \ln (x)}{x}$
81771	Evaluate the Limit	limit as x approaches infinity of (3x)/(7x-1)	$lim_{x \to \infty} \frac{3 x}{7 x - 1}$
81772	Find the Third Derivative	y=7^x+1102	$y = 7^{x} + 1102$
81773	Evaluate the Integral	integral from 0 to pi/3 of (9sin(theta)+9sin(theta)tan(theta)^2)/(sec(theta)^2) with respect to theta	$\int_{0}^{\frac{π}{3}} \frac{9 \sin (θ) + 9 \sin (θ) \tan^{2} (θ)}{\sec^{2} (θ)} d θ$
81774	Find the Antiderivative	f(x)=4-2/(x^3)	$f (x) = 4 - \frac{2}{x^{3}}$
81775	Find dy/dx	5xy+x^2=-y^2	$5 x y + x^{2} = - y^{2}$
81776	Evaluate the Integral	integral of (2e^x-2e^(-x))/((e^x+e^(-x))^2) with respect to x	$\int \frac{2 e^{x} - 2 e^{- x}}{{(e^{x} + e^{- x})}^{2}} d x$
81777	Evaluate the Integral	integral from pi/4 to pi/3 of (3tan(x)sec(x)+2cos(x)) with respect to x	$\int_{\frac{π}{4}}^{\frac{π}{3}} (3 \tan (x) \sec (x) + 2 \cos (x)) d x$
81778	Find dy/dw	x^2-y+z^2=w	$x^{2} - y + z^{2} = w$
81779	Find the Derivative - d/dx	y=(x-1/x)^2	$y = {(x - \frac{1}{x})}^{2}$
81780	Find the Inflection Points	f(x)=x^3-3/2x^2-36x	$f (x) = x^{3} - \frac{3}{2} x^{2} - 36 x$
81781	Evaluate the Integral	integral from 0 to 1 of x^6e^(-x^7) with respect to x	$\int_{0}^{1} x^{6} e^{- x^{7}} d x$
81782	Evaluate the Limit	limit as x approaches 0 of (e^(2x)-1)/x=2	$lim_{x \to 0} \frac{e^{2 x} - 1}{x} = 2$
81783	Evaluate the Limit	limit as x approaches infinity of 1/(x-2)+1	$lim_{x \to \infty} \frac{1}{x - 2} + 1$
81784	Find the Antiderivative	(x^5)/(x^2+1)	$\frac{x^{5}}{x^{2} + 1}$
81785	Find Where Increasing/Decreasing	((x-2)^3)/x	$\frac{{(x - 2)}^{3}}{x}$
81786	Evaluate the Integral	integral from 0 to 90^0 of cos(x) with respect to x	$\int_{0}^{90^{0}} \cos (x) d x$
81787	Find the Second Derivative	x^2y=4	$x^{2} y = 4$
81788	Evaluate the Limit	limit as x approaches infinity of (5x^2+x^-1)/(2x^3+5)	$lim_{x \to \infty} \frac{5 x^{2} + x^{- 1}}{2 x^{3} + 5}$
81789	Find dy/dx	y=xtan(x)	$y = x \tan (x)$
81790	Evaluate the Integral	integral from 1 to 2 of (3x^2-4x-2/(x^2)) with respect to x	$\int_{1}^{2} (3 x^{2} - 4 x - \frac{2}{x^{2}}) d x$
81791	Evaluate the Summation	sum from n=1 to infinity of (-4/3)(1/3)^(n-1)	$\sum_{n = 1}^{\infty} (- \frac{4}{3}) {(\frac{1}{3})}^{n - 1}$
81792	Find the Maximum/Minimum Value	f(x)=(x-1)^(1/3)	$f (x) = {(x - 1)}^{\frac{1}{3}}$
81793	Evaluate the Limit	limit as x approaches 0 of (9tan(x))/(-3x)	$lim_{x \to 0} \frac{9 \tan (x)}{- 3 x}$
81794	Find dy/dx	-x-y^3=2y^2-1-5x^3	$- x - y^{3} = 2 y^{2} - 1 - 5 x^{3}$
81795	Solve the Differential Equation	y'=y	$y' = y$
81796	Find the Derivative - d/dx	1-xe^y	$1 - x e^{y}$
81797	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of sin(x)^x	$lim_{x \to 0^{+}} {\sin (x)}^{x}$
81798	Integrate Using u-Substitution	integral of (x^2)/((1+x^3)^2) with respect to x	$\int \frac{x^{2}}{{(1 + x^{3})}^{2}} d x$
81799	Evaluate the Integral	integral of (x^3+1)/(x+2) with respect to x	$\int \frac{x^{3} + 1}{x + 2} d x$
81800	Find dy/dx	-xy-y^3=-x	$- x y - y^{3} = - x$