Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
84201	Evaluate the Integral	integral from 0 to pi/4 of xsec(x)^2 with respect to x	$\int_{0}^{\frac{π}{4}} x \sec^{2} (x) d x$
84202	Find dx/dy	4x^2y^7-2x=x^5+4y^3	$4 x^{2} y^{7} - 2 x = x^{5} + 4 y^{3}$
84203	Find the Integral	9/((x+2)^2)dx	$\frac{9}{{(x + 2)}^{2}} d x$
84204	Evaluate Using L'Hospital's Rule	limit as x approaches -1 of (4tan(-2-2x))/(e^(x+1)+x)	$lim_{x \to - 1} \frac{4 \tan (- 2 - 2 x)}{e^{x + 1} + x}$
84205	Find the Antiderivative	f(x)=4e^x+x	$f (x) = 4 e^{x} + x$
84206	Evaluate the Integral	integral of (4/x+sec(x)^2) with respect to x	$\int (\frac{4}{x} + \sec^{2} (x)) d x$
84207	Integrate Using u-Substitution	integral of 1/x with respect to x	$\int \frac{1}{x} d x$
84208	Evaluate the Limit	limit as x approaches infinity of (15x^4+x^2-1)/(3x^4+7x-8)	$lim_{x \to \infty} \frac{15 x^{4} + x^{2} - 1}{3 x^{4} + 7 x - 8}$
84209	Find the Maximum/Minimum Value	g(x) = cube root of x+4	$g (x) = \sqrt[3]{x + 4}$
84210	Evaluate the Integral	integral of 1/(x square root of 1-( natural log of x)^2) with respect to x	$\int \frac{1}{x \sqrt{1 - \ln^{2} (x)}} d x$
84211	Find the Second Derivative	f(x)=-1/2x^2+x^3+x^4-3/20x^5	$f (x) = - \frac{1}{2} x^{2} + x^{3} + x^{4} - \frac{3}{20} x^{5}$
84212	Find the Derivative of the Integral	F(x) = integral from -2 to cos(x) of 3t with respect to t	$F (x) = \int_{- 2}^{\cos (x)} 3 t d t$
84213	Evaluate the Integral	integral of (sec(8x)^2)/(tan(8x)-6) with respect to x	$\int \frac{\sec^{2} (8 x)}{\tan (8 x) - 6} d x$
84214	Find Where Increasing/Decreasing	f(x) = square root of x-1-4	$f (x) = \sqrt{x - 1} - 4$
84215	Integrate Using u-Substitution	integral of e^(-x^2) with respect to x	$\int e^{- x^{2}} d x$
84216	Evaluate the Integral	integral of (7u^(3/2)+2u^(1/2)) with respect to x	$\int (7 u^{\frac{3}{2}} + 2 u^{\frac{1}{2}}) d x$
84217	Evaluate the Limit	limit as x approaches pi of (2x^2-6xpi+4pi^2)/(x^2-pi^2)	$lim_{x \to π} \frac{2 x^{2} - 6 x π + 4 π^{2}}{x^{2} - π^{2}}$
84218	Find the Derivative - d/dx	-x^3+x+1/x	$- x^{3} + x + \frac{1}{x}$
84219	Find the Derivative - d/dx	Ce^(-x^3)	$C e^{- x^{3}}$
84220	Find the Maximum/Minimum Value	f(x)=x^5+x^4	$f (x) = x^{5} + x^{4}$
84221	Find dx/dy	e^(xy)=e^(4x)-e^(5y)	$e^{x y} = e^{4 x} - e^{5 y}$
84222	Find the Derivative - d/dx	y=cos(x^3-2x)	$y = \cos (x^{3} - 2 x)$
84223	Evaluate the Integral	integral of ((8+r)/r)^2 with respect to r	$\int {(\frac{8 + r}{r})}^{2} d r$
84224	Find the Tangent Line at (-2,16)	f(x)=-2x^3 at (-2,16)	$f (x) = - 2 x^{3}$ at $(- 2, 16)$
84225	Find the Maximum/Minimum Value	y=10cos((2pi)/3(x+1/4))	$y = 10 \cos (\frac{2 π}{3} (x + \frac{1}{4}))$
84226	Integrate Using u-Substitution	integral from 0 to 1 of x^2(1+2x^3)^5 with respect to x	$\int_{0}^{1} x^{2} {(1 + 2 x^{3})}^{5} d x$
84227	Find the Antiderivative	f(x)=(2x^4+3)/(x^2)	$f (x) = \frac{2 x^{4} + 3}{x^{2}}$
84228	Find dy/dx	y=(2+5x^3)/(1+2x)	$y = \frac{2 + 5 x^{3}}{1 + 2 x}$
84229	Determine if Continuous	f(x)=sec((pix)/4)	$f (x) = \sec (\frac{π x}{4})$
84230	Find the Second Derivative	f(x)=-1/2x^5-1/3x^-3-6x^2-1/5x	$f (x) = - \frac{1}{2} x^{5} - \frac{1}{3} x^{- 3} - 6 x^{2} - \frac{1}{5} x$
84231	Find the Derivative - d/dx	csc(x)+cot(x)	$\csc (x) + \cot (x)$
84232	Evaluate the Integral	integral of (-3csc(x)^2+4csc(2x)cot(2x)) with respect to x	$\int (- 3 \csc^{2} (x) + 4 \csc (2 x) \cot (2 x)) d x$
84233	Evaluate the Integral	integral of 44/(x^2 square root of x^2+16) with respect to x	$\int \frac{44}{x^{2} \sqrt{x^{2} + 16}} d x$
84234	Integrate Using u-Substitution	integral of 2xcos(x^2) with respect to x	$\int 2 x \cos (x^{2}) d x$
84235	Evaluate the Integral	integral from 0 to pi/4 of 3sec(theta)^4tan(theta)^4 with respect to theta	$\int_{0}^{\frac{π}{4}} 3 \sec^{4} (θ) \tan^{4} (θ) d θ$
84236	Integrate By Parts	integral of x/(e^x) with respect to x	$\int \frac{x}{e^{x}} d x$
84237	Find the Second Derivative	natural log of 1-x^2	$\ln (1 - x^{2})$
84238	Find the Derivative - d/dx	pi^( square root of x)	$π^{\sqrt{x}}$
84239	Evaluate the Integral	pi integral from 0 to 6 of (-x+6)^2 with respect to x	$π \int_{0}^{6} {(- x + 6)}^{2} d x$
84240	Integrate Using u-Substitution	integral of x/( square root of 1-x^4) with respect to x	$\int \frac{x}{\sqrt{1 - x^{4}}} d x$
84241	Find the Derivative - d/dx	(x^2+1)sin(3x-1)	$(x^{2} + 1) \sin (3 x - 1)$
84242	Find the Second Derivative	f(x)=x^2+x	$f (x) = x^{2} + x$
84243	Integrate Using u-Substitution	integral of 1/( square root of 2x) with respect to x	$\int \frac{1}{\sqrt{2 x}} d x$
84244	Find the Maximum/Minimum Value	f(x) = square root of x-5+2	$f (x) = \sqrt{x - 5} + 2$
84245	Evaluate the Integral	integral from pi/4 to pi/2 of (1-cos(2t))sin(2t) with respect to t	$\int_{\frac{π}{4}}^{\frac{π}{2}} (1 - \cos (2 t)) \sin (2 t) d t$
84246	Evaluate the Limit	limit as x approaches 0 of xtan(x+pi/2)	$lim_{x \to 0} x \tan (x + \frac{π}{2})$
84247	Find the Derivative - d/dx	y=( natural log of x)/(e^x)	$y = \frac{\ln (x)}{e^{x}}$
84248	Evaluate the Integral	integral of (2/( square root of x^3)) with respect to x	$\int (\frac{2}{\sqrt{x^{3}}}) d x$
84249	Find the Antiderivative	f(x)=x+cos(x)	$f (x) = x + \cos (x)$
84250	Find the Integral	1/( cube root of x^2)	$\frac{1}{\sqrt[3]{x^{2}}}$
84251	Evaluate Using Summation Formulas	limit as n approaches infinity of sum from i=1 to n of ((2i)/n)(2/n)	$lim_{n \to \infty} \sum_{i = 1}^{n} (\frac{2 i}{n}) (\frac{2}{n})$
84252	Determine if Continuous	f(x)=4e^(x-2)+ax-3a if x<2; x^3+ax^2+5 if x>=2	$f (x) = {\begin{cases} 4 e^{x - 2} + a x - 3 a & x < 2 \\ x^{3} + a x^{2} + 5 & x \geq 2 \end{cases}$
84253	Find the Antiderivative	1/( square root of 1+x)	$\frac{1}{\sqrt{1 + x}}$
84254	Find the Derivative - d/dx	2sin(2x)^4-3sin(4x)^3	$2 \sin^{4} (2 x) - 3 \sin^{3} (4 x)$
84255	Find the Derivative - d/dx	y=-7x^-5+4x^2-19x+2	$y = - 7 x^{- 5} + 4 x^{2} - 19 x + 2$
84256	Find the Derivative - d/dt	(70t)/((3t^2+8)^2)	$\frac{70 t}{{(3 t^{2} + 8)}^{2}}$
84257	Find the Derivative - d/dx	y=x^n(a+bx)^m	$y = x^{n} {(a + b x)}^{m}$
84258	Find dy/dx	-y+2xy=-3x	$- y + 2 x y = - 3 x$
84259	Find the Antiderivative	f(x)=2x^2+x	$f (x) = 2 x^{2} + x$
84260	Find the Derivative - d/dx	square root of (3x-2)^2-4	$\sqrt{{(3 x - 2)}^{2} - 4}$
84261	Evaluate the Limit	limit as x approaches (5pi)/(2^(-)) of x^2cot(x)	$lim_{x \to \frac{5 π}{2^{-}}} x^{2} \cot (x)$
84262	Find the Integral	1/(1+x^2)dx	$\frac{1}{1 + x^{2}} d x$
84263	Evaluate the Integral	integral from 1 to square root of 3 of 1/(6+6x^2) with respect to x	$\int_{1}^{\sqrt{3}} \frac{1}{6 + 6 x^{2}} d x$
84264	Evaluate the Integral	integral of 45sin(x)^3cos(x)^2 with respect to x	$\int 45 \sin^{3} (x) \cos^{2} (x) d x$
84265	Find the Antiderivative	1/(x^2(x+1))	$\frac{1}{x^{2} (x + 1)}$
84266	Find the Derivative - d/dx	2e^(x/2)	$2 e^{\frac{x}{2}}$
84267	Evaluate the Limit	limit as x approaches 3 of (x^2-x-6)/( square root of 5x-6-3)	$lim_{x \to 3} \frac{x^{2} - x - 6}{\sqrt{5 x - 6} - 3}$
84268	Find the Antiderivative	f(x)=sin(x)^4	$f (x) = \sin^{4} (x)$
84269	Use the Initial Value to Solve for c	y'=2xy , y=ce^(x^2) , y(0)=1	$y' = 2 x y$ , $y = c e^{x^{2}}$ , $y (0) = 1$
84270	Find the Derivative - d/dx	4e^x+4e^(-x)	$4 e^{x} + 4 e^{- x}$
84271	Evaluate the Integral	Evaluate integral of 12x^2 with respect to x	Evaluate $\int 12 x^{2} d x$
84272	Evaluate the Integral	integral from 1 to 3 of (2x^3-4x^-2) with respect to x	$\int_{1}^{3} (2 x^{3} - 4 x^{- 2}) d x$
84273	Find the Arc Length	theta=(4pi)/5 , r=9cm	$θ = \frac{4 π}{5}$ , $r = 9 cm$
84274	Find the Maximum/Minimum Value	y=8cos(pi/4x-pi/2)	$y = 8 \cos (\frac{π}{4} x - \frac{π}{2})$
84275	Evaluate the Integral	integral of 20 cube root of 3x-2 with respect to x	$\int 20 \sqrt[3]{3 x - 2} d x$
84276	Integrate By Parts	integral of natural log of x^2+1 with respect to x	$\int \ln (x^{2} + 1) d x$
84277	Find dx/dy	y=xe^(2x)	$y = x e^{2 x}$
84278	Evaluate the Integral	integral of (2x^2+4x-3)/(x^2) with respect to x	$\int \frac{(2 x^{2} + 4 x - 3)}{x^{2}} d x$
84279	Integrate By Parts	integral of x(x+2)^4 with respect to x	$\int x {(x + 2)}^{4} d x$
84280	Integrate By Parts	integral from 0 to infinity of xe^(-x) with respect to x	$\int_{0}^{\infty} x e^{- x} d x$
84281	Find the Critical Points	Let h(x)=(e^(2x))/(x-3)	Let $h (x) = \frac{e^{2 x}}{x - 3}$
84282	Find the Integral	xsin(xdx)	$x \sin (x d x)$
84283	Evaluate the Integral	2 integral from 0 to 1 of x^3 square root of 1-x^2 with respect to x	$2 \int_{0}^{1} x^{3} \sqrt{1 - x^{2}} d x$
84284	Find dy/dx	x^2+y^2-4=0	$x^{2} + y^{2} - 4 = 0$
84285	Find dy/dx	y=2x^2-x^2sin(x)	$y = 2 x^{2} - x^{2} \sin (x)$
84286	Find Where Increasing/Decreasing	f'(x)=x^2-2/x	$f' (x) = x^{2} - \frac{2}{x}$
84287	Evaluate the Limit	limit as x approaches negative infinity of square root of (4x^2+2x-1)/(9x^2-x-3)	$lim_{x \to - \infty} \sqrt{\frac{4 x^{2} + 2 x - 1}{9 x^{2} - x - 3}}$
84288	Evaluate the Integral	integral from -4 to 0 of (y/4+ square root of y+5) with respect to y	$\int_{- 4}^{0} (\frac{y}{4} + \sqrt{y + 5}) d y$
84289	Find the Derivative - d/dx	x^3+2x+1/pisin(pix)	$x^{3} + 2 x + \frac{1}{π} \sin (π x)$
84290	Find the Derivative - d/dx	y^2(6-2x)	$y^{2} (6 - 2 x)$
84291	Evaluate the Integral	integral from -1 to 0 of (y+ square root of y+2) with respect to y	$\int_{- 1}^{0} (y + \sqrt{y + 2}) d y$
84292	Evaluate the Integral	integral from 1 to 2 of (12/(x^2)-1) with respect to x	$\int_{1}^{2} (\frac{12}{x^{2}} - 1) d x$
84293	Find the Derivative - d/dx	y=cos(x)^4-sin(x)^4	$y = \cos^{4} (x) - \sin^{4} (x)$
84294	Evaluate from the Right	limit as x approaches 0 of square root of x	$lim_{x \to 0} \sqrt{x}$
84295	Find the Derivative - d/dx	2x square root of x+1	$2 x \sqrt{x + 1}$
84296	Find dy/dx	-x^2-y+5y^2=-5	$- x^{2} - y + 5 y^{2} = - 5$
84297	Evaluate the Limit	limit as x approaches 4 of (1+ cube root of x)(2-x^2+3x^3)	$lim_{x \to 4} (1 + \sqrt[3]{x}) (2 - x^{2} + 3 x^{3})$
84298	Evaluate the Integral	integral from 0 to a of 6x square root of a^2-x^2 with respect to x	$\int_{0}^{a} 6 x \sqrt{a^{2} - x^{2}} d x$
84299	Find the Derivative - d/dx	(e^x-1)^2	${(e^{x} - 1)}^{2}$
84300	Find the Derivative - d/dx	(2sin(x))/(sec(x))	$\frac{2 \sin (x)}{\sec (x)}$