Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
83601	Evaluate the Integral	integral of (12x^2)/( cube root of x^3+6) with respect to x	$\int \frac{12 x^{2}}{\sqrt[3]{x^{3} + 6}} d x$
83602	Find dy/dx	5^x+5^y=10	$5^{x} + 5^{y} = 10$
83603	Find the Derivative - d/dx	2x^3* cube root of x	$2 x^{3} \cdot \sqrt[3]{x}$
83604	Evaluate the Limit	limit as x approaches infinity of ( square root of 25x^2-7)/(x+2) is	$lim_{x \to \infty} \frac{\sqrt{25 x^{2} - 7}}{x + 2}$ is
83605	Find the Derivative - d/dx	(-y)/(x^2+y^2)	$\frac{- y}{x^{2} + y^{2}}$
83606	Evaluate the Integral	integral of 2x^2(x-5)^2 with respect to x	$\int 2 x^{2} {(x - 5)}^{2} d x$
83607	Evaluate the Limit	limit as x approaches infinity of (3x^2+20x)/(4x^2+9)	$lim_{x \to \infty} \frac{3 x^{2} + 20 x}{4 x^{2} + 9}$
83608	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (3tan(3x)-x^3)/(4 natural log of 1-2x-3x^3)	$lim_{x \to 0} \frac{3 \tan (3 x) - x^{3}}{4 \ln (1 - 2 x) - 3 x^{3}}$
83609	Find the Maximum/Minimum Value	f(x)=10/3x^3-x^2-8x+48	$f (x) = \frac{10}{3} x^{3} - x^{2} - 8 x + 48$
83610	Find dy/dx	x^3-y^3=6xy	$x^{3} - y^{3} = 6 x y$
83611	Evaluate the Integral	integral of ((-4x-4x^5)/(x^2)+5e^(7x)) with respect to x	$\int (\frac{- 4 x - 4 x^{5}}{x^{2}} + 5 e^{7 x}) d x$
83612	Find dy/dx	y=2cos(x)^3	$y = 2 \cos^{3} (x)$
83613	Evaluate the Limit	limit as x approaches infinity of 4x^3-x^4	$lim_{x \to \infty} 4 x^{3} - x^{4}$
83614	Evaluate the Integral	integral from 0 to 1 of xsin(pix^2) with respect to x	$\int_{0}^{1} x \sin (π x^{2}) d x$
83615	Find the Second Derivative	x*e^x	$x \cdot e^{x}$
83616	Evaluate the Integral	integral of (x^3)/(2x^4) with respect to x	$\int \frac{x^{3}}{2 x^{4}} d x$
83617	Evaluate the Summation	6 sum from p=4 to 8 of -6p+p^2	$6 \sum_{p = 4}^{8} - 6 p + p^{2}$
83618	Find dy/dx	square root of x+2y=5y	$\sqrt{x + 2 y} = 5 y$
83619	Find dy/dx	y=(sin(2x))/4	$y = \frac{\sin (2 x)}{4}$
83620	Find the Antiderivative	f(x)=4x-6x^2+1	$f (x) = 4 x - 6 x^{2} + 1$
83621	Find the Antiderivative	((x+2)^2)/(x^4)	$\frac{{(x + 2)}^{2}}{x^{4}}$
83622	Evaluate the Integral	integral of 2^(4x^2)x with respect to x	$\int 2^{4 x^{2}} x d x$
83623	Find the Derivative - d/dx	y=e^(6x^3+2x^2)	$y = e^{6 x^{3} + 2 x^{2}}$
83624	Evaluate the Integral	integral of 9/(theta^2)cos(9/theta) with respect to theta	$\int \frac{9}{θ^{2}} \cos (\frac{9}{θ}) d θ$
83625	Find the Derivative - d/dx	y=(e^(2x)-e^(-2x))/(e^(2x)+e^(-2x))	$y = \frac{e^{2 x} - e^{- 2 x}}{e^{2 x} + e^{- 2 x}}$
83626	Find the Antiderivative	(-9x^(4/5)+3x^-6+9x^3-15)dx	$(- 9 x^{\frac{4}{5}} + 3 x^{- 6} + 9 x^{3} - 15) d x$
83627	Find dy/dx	y=4cos(-5x^2)	$y = 4 \cos (- 5 x^{2})$
83628	Find the Antiderivative	f(x)=(x-1)/(x+2)	$f (x) = \frac{x - 1}{x + 2}$
83629	Find the Antiderivative	f(x)=-x	$f (x) = - x$
83630	Find the Derivative - d/dt	-1/t	$- \frac{1}{t}$
83631	Evaluate the Integral	integral of 1/(4^(2ax)) with respect to x	$\int \frac{1}{4^{2 a x}} d x$
83632	Find dx/dy	e^y+xy=e	$e^{y} + x y = e$
83633	Find dz/dx	z=(20x-xy)^3	$z = {(20 x - x y)}^{3}$
83634	Find the Integral	1/(x square root of x^2-1)	$\frac{1}{x \sqrt{x^{2} - 1}}$
83635	Find the Domain and Range	f(x)=x+2 if x<=2; x^2 if x>2	$f (x) = {\begin{cases} x + 2 & x \leq 2 \\ x^{2} & x > 2 \end{cases}$
83636	Find the Antiderivative	1/(2x^(1/2))	$\frac{1}{2 x^{\frac{1}{2}}}$
83637	Evaluate the Integral	integral of (2t^3+1)/((t^4+2t)^3) with respect to t	$\int \frac{2 t^{3} + 1}{{(t^{4} + 2 t)}^{3}} d t$
83638	Find dy/dx	(x+y)^5=y^3	${(x + y)}^{5} = y^{3}$
83639	Evaluate the Limit	limit as x approaches 0 of f(x)-g(x)	$lim_{x \to 0} f (x) - g (x)$
83640	Evaluate the Limit	limit as x approaches negative infinity of -(-1/(2 natural log of 5)*5^(-x^2))	$lim_{x \to - \infty} - (- \frac{1}{2 \ln (5)} \cdot 5^{- x^{2}})$
83641	Find the Derivative of the Integral	F(x) = integral from -2 to sin(x) of 3t with respect to t	$F (x) = \int_{- 2}^{\sin (x)} 3 t d t$
83642	Evaluate the Integral	integral of (2x)/( square root of 1-x^4) with respect to x	$\int \frac{2 x}{\sqrt{1 - x^{4}}} d x$
83643	Evaluate the Limit	limit as x approaches 0 of 2cos(x)+(x-4)/(x^2+1)	$lim_{x \to 0} 2 \cos (x) + \frac{x - 4}{x^{2} + 1}$
83644	Find the Derivative - d/dz	y = cube root of 1-8z	$y = \sqrt[3]{1 - 8 z}$
83645	Find the Antiderivative	3^(4-11x)	$3^{4 - 11 x}$
83646	Find the Antiderivative	f(x)=1/(4 square root of x)-x^2	$f (x) = \frac{1}{4 \sqrt{x}} - x^{2}$
83647	Evaluate the Integral	integral of 2/((6-x)^(3/2)) with respect to x	$\int \frac{2}{{(6 - x)}^{\frac{3}{2}}} d x$
83648	Evaluate the Limit	limit as x approaches infinity of (7x^3-4x+2x^2)/(5x^3-3x^2)	$lim_{x \to \infty} \frac{7 x^{3} - 4 x + 2 x^{2}}{5 x^{3} - 3 x^{2}}$
83649	Find the Derivative - d/dx	e^(2x)dx	$e^{2 x} d x$
83650	Find the Inflection Points	1/6x^4-2x^3-7x^2	$\frac{1}{6} x^{4} - 2 x^{3} - 7 x^{2}$
83651	Find the Third Derivative	f(x)=-1/3x^-2+1-3/20x^6+4/9x	$f (x) = - \frac{1}{3} x^{- 2} + 1 - \frac{3}{20} x^{6} + \frac{4}{9} x$
83652	Evaluate the Integral	integral from -4 to 3 of \|1/2x\| with respect to x	$\int_{- 4}^{3} \| \frac{1}{2} x \| d x$
83653	Find the Concavity	y=x^3	$y = x^{3}$
83654	Find dx/dy	y=arctan(4x^2-3)	$y = \arctan (4 x^{2} - 3)$
83655	Find the Derivative - d/dx	(x^4)/((6x+1)^3)	$\frac{x^{4}}{{(6 x + 1)}^{3}}$
83656	Evaluate the Integral	integral of (tan(x)^2+tan(x)^4) with respect to x	$\int (\tan^{2} (x) + \tan^{4} (x)) d x$
83657	Evaluate the Limit	limit as x approaches infinity of ((3x+9)(2x+7))/((x+1)(5x+4))	$lim_{x \to \infty} \frac{(3 x + 9) (2 x + 7)}{(x + 1) (5 x + 4)}$
83658	Evaluate the Integral	integral from 1 to e^2 of (x^3+1)/x with respect to x	$\int_{1}^{e^{2}} \frac{(x^{3} + 1)}{x} d x$
83659	Evaluate the Limit	limit as x approaches infinity of ( square root of 5x^2+2x)/x	$lim_{x \to \infty} \frac{\sqrt{5 x^{2} + 2 x}}{x}$
83660	Find the Slope	f(x)=4(x+3)	$f (x) = 4 (x + 3)$
83661	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ( square root of x)/( natural log of natural log of x)	$lim_{x \to \infty} \frac{\sqrt{x}}{\ln (\ln (x))}$
83662	Find the Derivative - d/dx	cube root of sin(x)	$\sqrt[3]{\sin (x)}$
83663	Evaluate the Limit	limit as x approaches -1/8 of (x+8x^2)/(x^2-1/64)	$lim_{x \to - \frac{1}{8}} \frac{x + 8 x^{2}}{x^{2} - \frac{1}{64}}$
83664	Find the Derivative - d/dx	1/( fifth root of 8x^2-2)	$\frac{1}{\sqrt[5]{8 x^{2} - 2}}$
83665	Integrate By Parts	integral from 0 to 1 of (x^2-1)e^x with respect to x	$\int_{0}^{1} (x^{2} - 1) e^{x} d x$
83666	Evaluate the Integral	integral from 0 to 4 of ( square root of x)^2 with respect to x	$\int_{0}^{4} {(\sqrt{x})}^{2} d x$
83667	Evaluate the Integral	integral of (2x^2+2x+11)/((2x+3)(x^2+4)) with respect to x	$\int \frac{2 x^{2} + 2 x + 11}{(2 x + 3) (x^{2} + 4)} d x$
83668	Find dy/dx	(3x+y)^5=4y^3	${(3 x + y)}^{5} = 4 y^{3}$
83669	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^x-cos(x)-2x)/(x^2-2x)	$lim_{x \to 0} \frac{e^{x} - \cos (x) - 2 x}{x^{2} - 2 x}$
83670	Find the Derivative - d/dx	(x^3)/(5+x^3)	$\frac{x^{3}}{5 + x^{3}}$
83671	Evaluate the Integral	integral from 0 to pi/6 of (sec(x)+tan(x))^2 with respect to x	$\int_{0}^{\frac{π}{6}} {(\sec (x) + \tan (x))}^{2} d x$
83672	Find the Derivative - d/dt	t^2( natural log of t)^4	$t^{2} \ln^{4} (t)$
83673	Find the Center and Radius	2x^2+2y^2+2z^2+x+y+z=9	$2 x^{2} + 2 y^{2} + 2 z^{2} + x + y + z = 9$
83674	Find the Antiderivative	cos(x)^4-sin(x)^4	$\cos^{4} (x) - \sin^{4} (x)$
83675	Find the Derivative - d/dx	y=arctan(x/6)+(3x-7)/(6(x^2+3))	$y = \arctan (\frac{x}{6}) + \frac{3 x - 7}{6 (x^{2} + 3)}$
83676	Find dy/dx	-xy+2-2x^3=3y^3	$- x y + 2 - 2 x^{3} = 3 y^{3}$
83677	Evaluate the Limit	limit as x approaches 6 from the right of x^3-cx	$lim_{x \to 6^{+}} x^{3} - c x$
83678	Evaluate the Limit	limit as x approaches 1 of (4 natural log of 3x-2)/(2-2x^2)	$lim_{x \to 1} \frac{4 \ln (3 x - 2)}{2 - 2 x^{2}}$
83679	Integrate Using u-Substitution	integral of cube root of 3-4x^2(-8x) with respect to x	$\int \sqrt[3]{3 - 4 x^{2}} (- 8 x) d x$
83680	Find the Antiderivative	x* square root of 1+x^2	$x \cdot \sqrt{1 + x^{2}}$
83681	Find dy/dx	-5x-y^2-4y+3y^3+x^2=0	$- 5 x - y^{2} - 4 y + 3 y^{3} + x^{2} = 0$
83682	Find dy/dx	y=1/( fifth root of 8x^2-2)	$y = \frac{1}{\sqrt[5]{8 x^{2} - 2}}$
83683	Evaluate the Limit	limit as x approaches 5 from the right of ( square root of x-5)/x	$lim_{x \to 5^{+}} \frac{\sqrt{x - 5}}{x}$
83684	Find the Integral	x*e^(x^2)	$x \cdot e^{x^{2}}$
83685	Find the Derivative - d/dx	fourth root of x^3+4x^2+7	$\sqrt[4]{x^{3} + 4 x^{2} + 7}$
83686	Find the Derivative - d/dx	y=( square root of 1-sin(x))/(x^2)	$y = \frac{\sqrt{1 - \sin (x)}}{x^{2}}$
83687	Find the Antiderivative	log base 2 of x	$\log_{2} (x)$
83688	Evaluate the Limit	limit as h approaches 0 of (2 cube root of 8+h-2 cube root of 8)/h	$lim_{h \to 0} \frac{2 \sqrt[3]{8 + h} - 2 \sqrt[3]{8}}{h}$
83689	Find dx/dy	y=xe^(-x)	$y = x e^{- x}$
83690	Evaluate the Limit	limit as x approaches negative infinity of (e^x+e^(-x))/2	$lim_{x \to - \infty} \frac{e^{x} + e^{- x}}{2}$
83691	Find dy/dx	y=5/(5x^2+5)	$y = \frac{5}{5 x^{2} + 5}$
83692	Find the Derivative - d/dx	d/(dx)(arcsin(x^4))	$\frac{d}{d x} (\arcsin (x^{4}))$
83693	Find dy/dx	y=cos(4x+5)	$y = \cos (4 x + 5)$
83694	Find the Antiderivative	x+e^x	$x + e^{x}$
83695	Find the Antiderivative	f(x)=3cos(x/3)+sin(3x)	$f (x) = 3 \cos (\frac{x}{3}) + \sin (3 x)$
83696	Evaluate the Integral	integral from 0 to 2 of (8z+4z^3-6z^2) with respect to z	$\int_{0}^{2} (8 z + 4 z^{3} - 6 z^{2}) d z$
83697	Integrate By Parts	integral of 2x with respect to x	$\int 2 x d x$
83698	Evaluate the Integral	integral of 5*5^(5x) with respect to x	$\int 5 \cdot 5^{5 x} d x$
83699	Integrate Using u-Substitution	integral of sin(2x)cos(2x) with respect to x	$\int \sin (2 x) \cos (2 x) d x$
83700	Evaluate the Summation	5 sum from t=0 to 4 of -3t+5	$5 \sum_{t = 0}^{4} - 3 t + 5$