Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
83201	Find the Derivative - d/dx	1/2x-sin(x)	$\frac{1}{2} x - \sin (x)$
83202	Find dy/dt	y=e^(5t)	$y = e^{5 t}$
83203	Find the Derivative - d/dx	3x^2 square root of 5x+3	$3 x^{2} \sqrt{5 x + 3}$
83204	Evaluate the Integral	integral from 0 to 1 of 2x^2cos(x) with respect to x	$\int_{0}^{1} 2 x^{2} \cos (x) d x$
83205	Evaluate the Limit	limit as x approaches -2 of ( cube root of x-6+2)/(x^3+8)	$lim_{x \to - 2} \frac{\sqrt[3]{x - 6} + 2}{x^{3} + 8}$
83206	Evaluate from the Left	limit as x approaches 0 of \|x\|	$lim_{x \to 0} \| x \|$
83207	Find the Third Derivative	x square root of x-1	$x \sqrt{x - 1}$
83208	Evaluate the Integral	integral of square root of 7-x^2 with respect to x	$\int \sqrt{7 - x^{2}} d x$
83209	Evaluate the Integral	integral of (-5x^-3-6) with respect to x	$\int (- 5 x^{- 3} - 6) d x$
83210	Evaluate the Integral	integral of 1/(x^2+y^2) with respect to y	$\int \frac{1}{x^{2} + y^{2}} d y$
83211	Find the Fourth Derivative	f(x)=x^5-2/(x^3)-4x+2 ?	$f (x) = x^{5} - \frac{2}{x^{3}} - 4 x + 2$ ?
83212	Find dy/dx	y=arctan(x/2)	$y = \arctan (\frac{x}{2})$
83213	Find the Maximum/Minimum Value	y=-2-4sin(pi/2(x-1/3))	$y = - 2 - 4 \sin (\frac{π}{2} (x - \frac{1}{3}))$
83214	Evaluate the Integral	integral from 0 to 1 of (2arctan(x))/(1+x^2) with respect to x	$\int_{0}^{1} \frac{2 \arctan (x)}{1 + x^{2}} d x$
83215	Find the Maximum/Minimum Value	f(x)=1/(x^2)	$f (x) = \frac{1}{x^{2}}$
83216	Find the Derivative - d/dx	f(x^3)	$f (x^{3})$
83217	Find the Derivative - d/dx	y=(2x)(3x^3)	$y = (2 x) (3 x^{3})$
83218	Find the Derivative - d/dx	square root of 1+x^4	$\sqrt{1 + x^{4}}$
83219	Find the Antiderivative	(sin(2x))/(sin(x))	$\frac{\sin (2 x)}{\sin (x)}$
83220	Find dy/dx	sin(x)-cos(y)-2=0	$\sin (x) - \cos (y) - 2 = 0$
83221	Find the Area Under the Curve	y=\|x^2-4\| y=0 y=5	$y = \| x^{2} - 4 \|$ $y = 0$ $y = 5$
83222	Find the Antiderivative	square root of x+ cube root of x	$\sqrt{x} + \sqrt[3]{x}$
83223	Evaluate the Integral	integral of (-3x^-3+2+3x^-2) with respect to x	$\int (- 3 x^{- 3} + 2 + 3 x^{- 2}) d x$
83224	Find the Antiderivative	1/2+3/4x^2-4/5x^3	$\frac{1}{2} + \frac{3}{4} x^{2} - \frac{4}{5} x^{3}$
83225	Integrate Using u-Substitution	integral of (csc(x)^2)/(cot(x)^3) with respect to x	$\int \frac{\csc^{2} (x)}{\cot^{3} (x)} d x$
83226	Evaluate the Integral	integral of (x^3+x) square root of x^4+2x^2 with respect to x	$\int (x^{3} + x) \sqrt{x^{4} + 2 x^{2}} d x$
83227	Find Where Increasing/Decreasing	y=(0.9)^(t-4)	$y = {(0.9)}^{t - 4}$
83228	Find Where Increasing/Decreasing	f(x)=3e^(x-1)+4	$f (x) = 3 e^{x - 1} + 4$
83229	Evaluate the Integral	integral of 1/x+1/(x^2) with respect to x	$\int \frac{1}{x} + \frac{1}{x^{2}} d x$
83230	Evaluate the Integral	integral of (3x^4-4+x^-2) with respect to x	$\int (3 x^{4} - 4 + x^{- 2}) d x$
83231	Evaluate the Limit	limit as x approaches 9 from the right of (x^2-13x+36)/(x-9)	$lim_{x \to 9^{+}} \frac{x^{2} - 13 x + 36}{x - 9}$
83232	Find the Critical Points	Let g(x)=(x^2-3)/(x+2)	Let $g (x) = \frac{x^{2} - 3}{x + 2}$
83233	Find the Derivative - d/dx	2/(x^3)+C	$\frac{2}{x^{3}} + C$
83234	Evaluate the Integral	integral from 0 to 4 of p/( square root of 9+p^2) with respect to p	$\int_{0}^{4} \frac{p}{\sqrt{9 + p^{2}}} d p$
83235	Find the Derivative - d/dx	-x^(3/2)	$- x^{\frac{3}{2}}$
83236	Find the Antiderivative	(x-1) square root of x	$(x - 1) \sqrt{x}$
83237	Find the Integral	1/( square root of x^2+1)	$\frac{1}{\sqrt{x^{2} + 1}}$
83238	Evaluate the Integral	- integral from 298 to 500 of 154.8/(500^2) with respect to x	$- \int_{298}^{500} \frac{154.8}{500^{2}} d x$
83239	Find the Derivative - d/dx	x^2(-3x^2-2)	$x^{2} (- 3 x^{2} - 2)$
83240	Evaluate the Integral	integral of 5x^3-3/x+1/(2 cube root of x) with respect to x	$\int 5 x^{3} - \frac{3}{x} + \frac{1}{2 \sqrt[3]{x}} d x$
83241	Find the Antiderivative	(2x+3)/(x^2)	$\frac{2 x + 3}{x^{2}}$
83242	Find the Inflection Points	f(x)=x^(1/3)(x^2-2x+1)	$f (x) = x^{\frac{1}{3}} (x^{2} - 2 x + 1)$
83243	Integrate Using Trig Substitution	integral of -1/(4x square root of 4-(2x)^2) with respect to x	$\int \frac{- 1}{4 x \sqrt{4 - {(2 x)}^{2}}} d x$
83244	Evaluate the Integral	integral of (-2x+3x^-3-4) with respect to x	$\int (- 2 x + 3 x^{- 3} - 4) d x$
83245	Evaluate the Limit	limit as x approaches 0 of (sin(3x)-tan(2x))/(5x)	$lim_{x \to 0} \frac{\sin (3 x) - \tan (2 x)}{5 x}$
83246	Integrate Using u-Substitution	integral of 1/(4+x^2) with respect to x	$\int \frac{1}{4 + x^{2}} d x$
83247	Find the Integral	x^2e^xdx	$x^{2} e^{x} d x$
83248	Find the Percentage Rate of Change	y=(0.98)^x	$y = {(0.98)}^{x}$
83249	Integrate Using u-Substitution	integral of 1/( square root of 1-4x^2) with respect to x	$\int \frac{1}{\sqrt{1 - 4 x^{2}}} d x$
83250	Find the Derivative - d/dx	y=-3/x	$y = \frac{- 3}{x}$
83251	Evaluate the Limit	limit as x approaches 0 of (2sin(x))/(tan(x))	$lim_{x \to 0} \frac{2 \sin (x)}{\tan (x)}$
83252	Find the Third Derivative	y=-1/24x^-4-3/20x-x^3+5/18	$y = - \frac{1}{24} x^{- 4} - \frac{3}{20} x - x^{3} + \frac{5}{18}$
83253	Evaluate the Integral	integral from 0 to 1 of (x+2)(3x^2+12x+1)^(1/2) with respect to x	$\int_{0}^{1} (x + 2) {(3 x^{2} + 12 x + 1)}^{\frac{1}{2}} d x$
83254	Find the Antiderivative	1/x-2x	$\frac{1}{x} - 2 x$
83255	Find the Derivative - d/dx	1+2x^2	$1 + 2 x^{2}$
83256	Find dy/dx	x^3-y^3=y	$x^{3} - y^{3} = y$
83257	Find the Critical Points	Let f(x)=(x+1)/(x-3)	Let $f (x) = \frac{x + 1}{x - 3}$
83258	Find the Antiderivative	1/(2 square root of x+1)	$\frac{1}{2 \sqrt{x + 1}}$
83259	Evaluate the Limit	limit as x approaches negative infinity of (x^2+6x+9)/(x^2+6x+9)	$lim_{x \to - \infty} \frac{x^{2} + 6 x + 9}{x^{2} + 6 x + 9}$
83260	Find the Derivative - d/dt	y = natural log of (t+1)^2	$y = \ln ({(t + 1)}^{2})$
83261	Find dy/dx	-xy+4-3x^2=y^3	$- x y + 4 - 3 x^{2} = y^{3}$
83262	Find the Antiderivative	2^x+x	$2^{x} + x$
83263	Evaluate the Limit	limit as x approaches 2pi from the right of xcsc(x)	$lim_{x \to {(2 π)}^{+}} x \csc (x)$
83264	Find the Center and Radius	x^2+y^2-6x=-4y+68	$x^{2} + y^{2} - 6 x = - 4 y + 68$
83265	Find the Second Derivative	x^2y-2=5x+y	$x^{2} y - 2 = 5 x + y$
83266	Find the Derivative - d/dx	x^2\|x\|	$x^{2} \| x \|$
83267	Find the Antiderivative	x^3+(x^2)/2	$x^{3} + \frac{x^{2}}{2}$
83268	Evaluate the Integral	integral from -2 to 2 of square root of 2^2-x^2 with respect to x	$\int_{- 2}^{2} \sqrt{2^{2} - x^{2}} d x$
83269	Evaluate the Integral	integral of (-3 square root of x-6 fourth root of x) with respect to x	$\int (- 3 \sqrt{x} - 6 \sqrt[4]{x}) d x$
83270	Evaluate the Integral	integral of 3/(4 square root of x^3) with respect to x	$\int \frac{3}{4 \sqrt{x^{3}}} d x$
83271	Find the Antiderivative	f(x)=tan(x)(4cos(x)+8sec(x))	$f (x) = \tan (x) (4 \cos (x) + 8 \sec (x))$
83272	Find the Derivative - d/dx	2e^x+2e^(-x)	$2 e^{x} + 2 e^{- x}$
83273	Find dy/dx	3x^3-xy^3+3-4y^3=0	$3 x^{3} - x y^{3} + 3 - 4 y^{3} = 0$
83274	Find the Center and Radius	x^2+y^2+x-y+6=0	$x^{2} + y^{2} + x - y + 6 = 0$
83275	Find the Maximum/Minimum Value	y=-1/5(x-5)^2-2	$y = - \frac{1}{5} {(x - 5)}^{2} - 2$
83276	Find the Derivative - d/dt	y=e^(sin(t))	$y = e^{\sin (t)}$
83277	Integrate Using u-Substitution	integral of 1/(x^2+4) with respect to x	$\int \frac{1}{x^{2} + 4} d x$
83278	Find the Antiderivative	1/(e^(2-5x))	$\frac{1}{e^{2 - 5 x}}$
83279	Find the Derivative - d/dx	-(6x^2)/(2y-1)	$- \frac{6 x^{2}}{2 y - 1}$
83280	Evaluate the Integral	Evaluate integral of -6x with respect to x	Evaluate $\int - 6 x d x$
83281	Evaluate the Limit	limit as x approaches -2 of (4)(x^2+4x-5)	$lim_{x \to - 2} (4) (x^{2} + 4 x - 5)$
83282	Find the Derivative - d/dx	tan(x^2)^2	$\tan^{2} (x^{2})$
83283	Evaluate Using L'Hospital's Rule	limit as x approaches -1 of (3 natural log of 3x+4)/(3tan(2x+2))	$lim_{x \to - 1} \frac{3 \ln (3 x + 4)}{3 \tan (2 x + 2)}$
83284	Find the Derivative - d/dx	1+1/(2(x+1)^(1/2))	$1 + \frac{1}{2 {(x + 1)}^{\frac{1}{2}}}$
83285	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of (1/x)^x	$lim_{x \to 0^{+}} {(\frac{1}{x})}^{x}$
83286	Evaluate the Summation	sum from k=2 to 5 of k^2+k-2	$\sum_{k = 2}^{5} k^{2} + k - 2$
83287	Find dy/dx	y=3 square root of 2x^2-x-4	$y = 3 \sqrt{2 x^{2} - x - 4}$
83288	Find the Derivative - d/dx	arcsin(e^(3x))	$\arcsin (e^{3 x})$
83289	Find dy/dx	f(x)=e^(xy)	$f (x) = e^{x y}$
83290	Evaluate the Limit	limit as x approaches 0 of (5x^4-3x^3+7x+2)^5	$lim_{x \to 0} {(5 x^{4} - 3 x^{3} + 7 x + 2)}^{5}$
83291	Evaluate the Integral	integral of (3x^3)(3x^2) with respect to x	$\int (3 x^{3}) (3 x^{2}) d x$
83292	Evaluate the Integral	integral from -5 to 1 of (-5x+4e^(-x)) with respect to x	$\int_{- 5}^{1} (- 5 x + 4 e^{- x}) d x$
83293	Evaluate the Integral	integral of (2x+1)e^(x^2+x) with respect to x	$\int (2 x + 1) e^{x^{2} + x} d x$
83294	Find the Integral	xsin(3x)	$x \sin (3 x)$
83295	Find dy/dx	-4y+4x^3+y^2=0	$- 4 y + 4 x^{3} + y^{2} = 0$
83296	Find the Domain and Range	f(x)=4-x^2,x<0; x-2,x>=0	$f (x) = {\begin{cases} 4 - x^{2}, x < 0 \\ x - 2, x \geq 0 \end{cases}$
83297	Find the Derivative - d/dx	-1/(4(x+1)^(3/2))	$\frac{- 1}{4 {(x + 1)}^{\frac{3}{2}}}$
83298	Find the Integral	xy^2	$x y^{2}$
83299	Find the Inflection Points	1/15x^6+x^5+25/6x^4	$\frac{1}{15} x^{6} + x^{5} + \frac{25}{6} x^{4}$
83300	Evaluate the Limit	limit as x approaches infinity of (7x^3-4x+2x^6)/(5x^9-3x^2)	$lim_{x \to \infty} \frac{7 x^{3} - 4 x + 2 x^{6}}{5 x^{9} - 3 x^{2}}$