Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
85201	Find Where Increasing/Decreasing	f(x)=-x^4-9x^3-24x^2-16x	$f (x) = - x^{4} - 9 x^{3} - 24 x^{2} - 16 x$
85202	Integrate Using u-Substitution	integral from 0 to 2 of square root of 4-x^2 with respect to x	$\int_{0}^{2} \sqrt{4 - x^{2}} d x$
85203	Evaluate the Integral	integral from 0 to a^(1/2) of x^3 square root of a^2-x^4 with respect to x	$\int_{0}^{a^{\frac{1}{2}}} x^{3} \sqrt{a^{2} - x^{4}} d x$
85204	Find the Derivative - d/dx	-1/(2 square root of x)	$- \frac{1}{2 \sqrt{x}}$
85205	Find dy/dx	y=-5(2x+3)^3	$y = - 5 {(2 x + 3)}^{3}$
85206	Find the Derivative - d/dx	1/((x^2+1)^(3/2))	$\frac{1}{{(x^{2} + 1)}^{\frac{3}{2}}}$
85207	Evaluate the Limit	limit as x approaches -1 of (x^2+yx+z)/(x^2-1)=3	$lim_{x \to - 1} \frac{x^{2} + y x + z}{x^{2} - 1} = 3$
85208	Evaluate the Integral	integral of (-6+x^3) with respect to x	$\int (- 6 + x^{3}) d x$
85209	Evaluate the Integral	integral of xe^x+e^x with respect to x	$\int x e^{x} + e^{x} d x$
85210	Evaluate the Integral	integral from 0 to 1 of (x-1)/(x+1) with respect to x	$\int_{0}^{1} \frac{x - 1}{x + 1} d x$
85211	Find the Derivative - d/dy	1/(x^2+y^2)	$\frac{1}{x^{2} + y^{2}}$
85212	Evaluate the Limit	limit as x approaches 3 of (2x^2-5x-12)/(6-x-x^2)	$lim_{x \to 3} \frac{2 x^{2} - 5 x - 12}{6 - x - x^{2}}$
85213	Find the Derivative - d/dx	y=1/( square root of 1-x^2)	$y = \frac{1}{\sqrt{1 - x^{2}}}$
85214	Find the Derivative - d/dx	-1/( square root of 1-x^2)	$- \frac{1}{\sqrt{1 - x^{2}}}$
85215	Evaluate the Integral	integral from pi/6 to pi/2 of cos(x) with respect to x	$\int_{\frac{π}{6}}^{\frac{π}{2}} \cos (x) d x$
85216	Evaluate the Integral	integral from 1 to 2 of 2x(1+x^2) with respect to x	$\int_{1}^{2} 2 x (1 + x^{2}) d x$
85217	Find the Derivative - d/dx	(x^3-2x^2+x-1)/(x-2)	$\frac{x^{3} - 2 x^{2} + x - 1}{x - 2}$
85218	Find the Derivative - d/dy	x*y	$x \cdot y$
85219	Evaluate the Integral	integral from pi/2 to (3pi)/2 of xsin(x) with respect to x	$\int_{\frac{π}{2}}^{\frac{3 π}{2}} x \sin (x) d x$
85220	Find the Percentage Rate of Change	w(t)=700(0.995)^t	$w (t) = 700 {(0.995)}^{t}$
85221	Find the Antiderivative	square root of 5-x	$\sqrt{5 - x}$
85222	Evaluate the Integral	integral from -3 to 4 of (2e^(-3x)-3e^x) with respect to x	$\int_{- 3}^{4} (2 e^{- 3 x} - 3 e^{x}) d x$
85223	Find the Critical Points	Let h(x)=e^(2x-6)-e	Let $h (x) = e^{2 x - 6} - e$
85224	Find the Absolute Max and Min over the Interval	f(x)=\|x\|-3\|x+1\| , [-2,2]	$f (x) = \| x \| - 3 \| x + 1 \|$ , $[- 2, 2]$
85225	Find dx/dy	tan(xy)=x	$\tan (x y) = x$
85226	Find the Derivative of the Integral	integral from -19 to x^2 of (t-169)^92(5t-245)^37 with respect to t	$\int_{- 19}^{x^{2}} {(t - 169)}^{92} {(5 t - 245)}^{37} d t$
85227	Find dy/dx	y = square root of x^2+2x-1	$y = \sqrt{x^{2} + 2 x - 1}$
85228	Integrate Using u-Substitution	integral of square root of 1+x^2 with respect to x	$\int \sqrt{1 + x^{2}} d x$
85229	Evaluate the Integral	integral of -1/(x^2) with respect to x	$\int \frac{- 1}{x^{2}} d x$
85230	Find the Derivative - d/dx	y=((x^2+1)^2)/(2x^2)	$y = \frac{{(x^{2} + 1)}^{2}}{2 x^{2}}$
85231	Find the Second Derivative	y=-1/5x^-4+1/2x^3-3x^-1	$y = - \frac{1}{5} x^{- 4} + \frac{1}{2} x^{3} - 3 x^{- 1}$
85232	Find Where Increasing/Decreasing	f(x)=-((x-2)^2)/((x-1)^2)	$f (x) = - \frac{{(x - 2)}^{2}}{{(x - 1)}^{2}}$
85233	Find the Derivative - d/dx	2e^(2x)-e^(-x)	$2 e^{2 x} - e^{- x}$
85234	Evaluate the Integral	integral of (3(1-tan(x)^2))/(sec(x)^2) with respect to x	$\int \frac{3 (1 - \tan^{2} (x))}{\sec^{2} (x)} d x$
85235	Find dy/dx	x^2=4y^3+5y^2	$x^{2} = 4 y^{3} + 5 y^{2}$
85236	Find the Antiderivative	fifth root of x-2e^x	$\sqrt[5]{x} - 2 e^{x}$
85237	Evaluate the Integral	integral of (2 square root of x^3+7 cube root of x^2) with respect to x	$\int (2 \sqrt{x^{3}} + 7 \sqrt[3]{x^{2}}) d x$
85238	Find the Derivative - d/dt	17/2-3/2cos((pit)/6)	$\frac{17}{2} - \frac{3}{2} \cos (\frac{π t}{6})$
85239	Find the Center and Radius	x^2-10x=-y^2+16y-40	$x^{2} - 10 x = - y^{2} + 16 y - 40$
85240	Find dx/dy	(x+y)^2(x-y)^2=x^4+y^4	${(x + y)}^{2} {(x - y)}^{2} = x^{4} + y^{4}$
85241	Evaluate the Integral	integral of (-3x^-2+4+6x^3) with respect to x	$\int (- 3 x^{- 2} + 4 + 6 x^{3}) d x$
85242	Find the Antiderivative	f(x)=7-6x^2+12x^3	$f (x) = 7 - 6 x^{2} + 12 x^{3}$
85243	Evaluate the Integral	e^( integral of -1 with respect to x)	$e^{\int - 1 d x}$
85244	Evaluate the Summation	4 sum from k=3 to 6 of -k^2+2k	$4 \sum_{k = 3}^{6} - k^{2} + 2 k$
85245	Find dy/dx	y=(4x^3)/(2x^2-5)	$y = \frac{4 x^{3}}{2 x^{2} - 5}$
85246	Evaluate the Limit	limit as x approaches 3 of (x+9)/(5-x)	$lim_{x \to 3} \frac{x + 9}{5 - x}$
85247	Find dx/dy	y=(4x^3)/(2x^2-5)	$y = \frac{4 x^{3}}{2 x^{2} - 5}$
85248	Evaluate the Integral	4 integral of 1/(1-x^2) with respect to x	$4 \int \frac{1}{1 - x^{2}} d x$
85249	Find the Derivative - d/dx	3e^x-e^(2x)	$3 e^{x} - e^{2 x}$
85250	Find the Derivative - d/dx	(cos(x)^2)	$(\cos^{2} (x))$
85251	Find the Derivative - d/dx	10-1/5(x-6)^2	$10 - \frac{1}{5} {(x - 6)}^{2}$
85252	Evaluate the Limit	limit as x approaches 1/2 of (2x-5)/7	$lim_{x \to \frac{1}{2}} \frac{2 x - 5}{7}$
85253	Find the Derivative - d/df	f(x)^2	$f {(x)}^{2}$
85254	Find the Antiderivative	e^(2x-1)*y^-2	$e^{2 x - 1} \cdot y^{- 2}$
85255	Find the Derivative - d/dx	y=( square root of x^3+ square root of x^5)^n	$y = {(\sqrt{x^{3}} + \sqrt{x^{5}})}^{n}$
85256	Integrate Using u-Substitution	integral of xe^(x^2) with respect to x	$\int x e^{x^{2}} d x$
85257	Integrate Using u-Substitution	integral from 0 to 1 of cube root of 1+7x with respect to x	$\int_{0}^{1} \sqrt[3]{1 + 7 x} d x$
85258	Integrate Using u-Substitution	integral of (( natural log of x)^2)/x with respect to x	$\int \frac{\ln^{2} (x)}{x} d x$
85259	Integrate Using u-Substitution	integral of e^(-x) with respect to x	$\int e^{- x} d x$
85260	Integrate Using u-Substitution	integral of (e^( square root of x))/( square root of x) with respect to x	$\int \frac{e^{\sqrt{x}}}{\sqrt{x}} d x$
85261	Integrate Using u-Substitution	integral of x^2 square root of x^3+1 with respect to x	$\int x^{2} \sqrt{x^{3} + 1} d x$
85262	Integrate Using u-Substitution	integral of x square root of x+2 with respect to x	$\int x \sqrt{x + 2} d x$
85263	Integrate Using u-Substitution	integral of x/(x^2+1) with respect to x	$\int \frac{x}{x^{2} + 1} d x$
85264	Integrate Using u-Substitution	integral from 0 to 1 of x square root of 1-x^2 with respect to x	$\int_{0}^{1} x \sqrt{1 - x^{2}} d x$
85265	Integrate Using u-Substitution	integral of x/( square root of 1-x^2) with respect to x	$\int \frac{x}{\sqrt{1 - x^{2}}} d x$
85266	Integrate Using u-Substitution	integral of x square root of x+1 with respect to x	$\int x \sqrt{x + 1} d x$
85267	Integrate Using u-Substitution	integral of sin(t) square root of 1+cos(t) with respect to t	$\int \sin (t) \sqrt{1 + \cos (t)} d t$
85268	Integrate Using u-Substitution	integral of x^3e^(x^4) with respect to x	$\int x^{3} e^{x^{4}} d x$
85269	Integrate Using u-Substitution	integral of e^(2x) with respect to x	$\int e^{2 x} d x$
85270	Integrate Using u-Substitution	integral of x^3 square root of x^2+1 with respect to x	$\int x^{3} \sqrt{x^{2} + 1} d x$
85271	Integrate Using u-Substitution	integral of x^2e^(x^3) with respect to x	$\int x^{2} e^{x^{3}} d x$
85272	Integrate Using u-Substitution	integral of (x^2)/((1+x^3)^2) with respect to x	$\int \frac{x^{2}}{{(1 + x^{3})}^{2}} d x$
85273	Integrate Using u-Substitution	integral of (sin( square root of x))/( square root of x) with respect to x	$\int \frac{\sin (\sqrt{x})}{\sqrt{x}} d x$
85274	Integrate Using u-Substitution	integral of x^2 square root of 1-x with respect to x	$\int x^{2} \sqrt{1 - x} d x$
85275	Integrate Using u-Substitution	integral of x square root of 1-x^2 with respect to x	$\int x \sqrt{1 - x^{2}} d x$
85276	Integrate Using u-Substitution	integral of xe^x with respect to x	$\int x e^{x} d x$
85277	Integrate Using u-Substitution	integral of x square root of 4-x^2 with respect to x	$\int x \sqrt{4 - x^{2}} d x$
85278	Integrate Using u-Substitution	integral of x/( square root of x+1) with respect to x	$\int \frac{x}{\sqrt{x + 1}} d x$
85279	Integrate Using u-Substitution	integral of (1+1/x)^3(1/(x^2)) with respect to x	$\int {(1 + \frac{1}{x})}^{3} (\frac{1}{x^{2}}) d x$
85280	Integrate Using u-Substitution	integral of xe^(-x^2) with respect to x	$\int x e^{- x^{2}} d x$
85281	Integrate Using u-Substitution	integral of 1/(x^2) with respect to x	$\int \frac{1}{x^{2}} d x$
85282	Integrate Using u-Substitution	integral of 5x cube root of 1-x^2 with respect to x	$\int 5 x \sqrt[3]{1 - x^{2}} d x$
85283	Integrate Using u-Substitution	integral of ( natural log of x)/x with respect to x	$\int \frac{\ln (x)}{x} d x$
85284	Integrate Using u-Substitution	integral of 1/(x natural log of x) with respect to x	$\int \frac{1}{x \ln (x)} d x$
85285	Integrate Using u-Substitution	integral of 125x^4sec(5x^5-4)*tan(5x^5-4) with respect to x	$\int 125 x^{4} \sec (5 x^{5} - 4) \cdot \tan (5 x^{5} - 4) d x$
85286	Integrate Using u-Substitution	integral from 0 to 1 of cos((pit)/2) with respect to t	$\int_{0}^{1} \cos (\frac{π t}{2}) d t$
85287	Integrate Using u-Substitution	integral of x^2(x^3-1)^4 with respect to x	$\int x^{2} {(x^{3} - 1)}^{4} d x$
85288	Integrate Using u-Substitution	integral of x^3(x^4+3)^2 with respect to x	$\int x^{3} {(x^{4} + 3)}^{2} d x$
85289	Integrate Using u-Substitution	integral of x square root of 2x+1 with respect to x	$\int x \sqrt{2 x + 1} d x$
85290	Integrate Using u-Substitution	integral of sin(x)^2 with respect to x	$\int \sin^{2} (x) d x$
85291	Integrate Using u-Substitution	integral of x square root of x-1 with respect to x	$\int x \sqrt{x - 1} d x$
85292	Integrate Using u-Substitution	integral of sin(x)^2 with respect to x	$\int \sin^{2} (x) d x$
85293	Integrate Using u-Substitution	integral of x/( square root of x^2+1) with respect to x	$\int \frac{x}{\sqrt{x^{2} + 1}} d x$
85294	Integrate Using u-Substitution	integral of x(2x+5)^8 with respect to x	$\int x {(2 x + 5)}^{8} d x$
85295	Integrate Using u-Substitution	integral of 1/(x natural log of x) with respect to x	$\int \frac{1}{x \ln (x)} d x$
85296	Integrate Using u-Substitution	integral from 1 to 4 of (e^( square root of x))/( square root of x) with respect to x	$\int_{1}^{4} \frac{e^{\sqrt{x}}}{\sqrt{x}} d x$
85297	Integrate Using u-Substitution	integral of natural log of x with respect to x	$\int \ln (x) d x$
85298	Integrate Using u-Substitution	integral of 1/(x^2) with respect to x	$\int \frac{1}{x^{2}} d x$
85299	Integrate Using u-Substitution	integral of cos(x)^2 with respect to x	$\int \cos^{2} (x) d x$
85300	Integrate Using u-Substitution	integral of cos(x)^3sin(x) with respect to x	$\int \cos^{3} (x) \sin (x) d x$