Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
80801	Find Where Increasing/Decreasing	x/(x+3)	$\frac{x}{x + 3}$
80802	Find the Antiderivative	f(x)=( square root of 2-6x)^5	$f (x) = {(\sqrt{2} - 6 x)}^{5}$
80803	Evaluate the Integral	1/pi integral from negative infinity to infinity of 1/(1+x^2) with respect to x	$\frac{1}{π} \int_{- \infty}^{\infty} \frac{1}{1 + x^{2}} d x$
80804	Find the Absolute Max and Min over the Interval	f(x)=arctan(x^2) on -2 , 2	$f (x) = \arctan (x^{2})$ on $- 2$ , $2$
80805	Find dy/dx	y=(2x+3)^3 square root of 4x^3-1	$y = {(2 x + 3)}^{3} \sqrt{4 x^{3} - 1}$
80806	Find dv/dr	v=4/3pir^3	$v = \frac{4}{3} π r^{3}$
80807	Evaluate the Limit	limit as x approaches 0 of 5xcsc(2x)	$lim_{x \to 0} 5 x \csc (2 x)$
80808	Find the Maximum/Minimum Value	f(x)=10+12x-3x^2-2x^3	$f (x) = 10 + 12 x - 3 x^{2} - 2 x^{3}$
80809	Find the Antiderivative	f(x)=-3 cube root of x	$f (x) = - 3 \sqrt[3]{x}$
80810	Find Where Increasing/Decreasing	f(x)=2/5x^5+x^4-32x^3+10	$f (x) = \frac{2}{5} x^{5} + x^{4} - 32 x^{3} + 10$
80811	Find the Derivative - d/dx	square root of x^3+3x^2	$\sqrt{x^{3} + 3 x^{2}}$
80812	Find the Antiderivative	f(x)=4x+1/(x^2)	$f (x) = 4 x + \frac{1}{x^{2}}$
80813	Evaluate the Limit	limit as x approaches 2 of 4^(3x-1)	$lim_{x \to 2} 4^{3 x - 1}$
80814	Evaluate the Integral	integral of 5x^3e^(2-3x^4) with respect to x	$\int 5 x^{3} e^{2 - 3 x^{4}} d x$
80815	Find dy/dx	y=sin(x)^( natural log of x)	$y = {\sin (x)}^{\ln (x)}$
80816	Find the Antiderivative	f(x)=1+1/(x^4)	$f (x) = 1 + \frac{1}{x^{4}}$
80817	Evaluate the Integral	integral of (2x+1)/(9+16x^2) with respect to x	$\int \frac{2 x + 1}{9 + 16 x^{2}} d x$
80818	Evaluate the Limit	limit as x approaches -5 of (-8\|x\|+40)/(2x+10)	$lim_{x \to - 5} \frac{- 8 \| x \| + 40}{2 x + 10}$
80819	Find the Antiderivative	-1/x	$\frac{- 1}{x}$
80820	Find Where Increasing/Decreasing	x^5+x^4	$x^{5} + x^{4}$
80821	Evaluate the Integral	integral from 0 to 1 of x^2*2^x with respect to x	$\int_{0}^{1} x^{2} \cdot 2^{x} d x$
80822	Find the Maximum/Minimum Value	f(x)=x^4+4x^2+1	$f (x) = x^{4} + 4 x^{2} + 1$
80823	Find the Antiderivative	f(x)=1/7	$f (x) = \frac{1}{7}$
80824	Find the Derivative - d/dx	y=10x^(4/5)	$y = 10 x^{\frac{4}{5}}$
80825	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 16x^2+3)/(2x+5)	$lim_{x \to - \infty} \frac{\sqrt{16 x^{2} + 3}}{2 x + 5}$
80826	Find the Center and Radius	x^2+(y+1/5)^2=9/25	$x^{2} + {(y + \frac{1}{5})}^{2} = \frac{9}{25}$
80827	Integrate Using u-Substitution	integral of x square root of 4-x with respect to x	$\int x \sqrt{4 - x} d x$
80828	Find the Critical Points	f(x) = square root of x^3+3x^2	$f (x) = \sqrt{x^{3} + 3 x^{2}}$
80829	Evaluate the Limit	limit as x approaches 0 of (x^2+x)/(2x)	$lim_{x \to 0} \frac{x^{2} + x}{2 x}$
80830	Evaluate the Integral	integral of 6x^4(2-3x^5)^7 with respect to x	$\int 6 x^{4} {(2 - 3 x^{5})}^{7} d x$
80831	Evaluate the Limit	limit as x approaches 2/3 of square root of 9x+19	$lim_{x \to \frac{2}{3}} \sqrt{9 x + 19}$
80832	Evaluate the Limit	limit as x approaches -2 of (-3x^3-24)/(x^2+x-2)	$lim_{x \to - 2} \frac{- 3 x^{3} - 24}{x^{2} + x - 2}$
80833	Integrate Using u-Substitution	integral of 5x cube root of 1-x^2 with respect to x	$\int 5 x \sqrt[3]{1 - x^{2}} d x$
80834	Evaluate the Integral	integral of ( cube root of x^4)/4 with respect to x	$\int \frac{\sqrt[3]{x^{4}}}{4} d x$
80835	Evaluate the Limit	limit as x approaches infinity of (x-5)/( cube root of 27x^3+12)	$lim_{x \to \infty} \frac{x - 5}{\sqrt[3]{27 x^{3} + 12}}$
80836	Find the Maximum/Minimum Value	f(x)=-5x^4+5x^3-10	$f (x) = - 5 x^{4} + 5 x^{3} - 10$
80837	Evaluate the Limit	limit as x approaches -1 of (-5x^3-5)/(x^2-5x-6)	$lim_{x \to - 1} \frac{- 5 x^{3} - 5}{x^{2} - 5 x - 6}$
80838	Find the Second Derivative	(x^2-1)/x	$\frac{x^{2} - 1}{x}$
80839	Find the Derivative - d/dx	y = cube root of x^2(2x-x^2)	$y = \sqrt[3]{x^{2}} (2 x - x^{2})$
80840	Find the Inflection Points	f(x)=-1/6x^6-2x^5	$f (x) = - \frac{1}{6} x^{6} - 2 x^{5}$
80841	Find the Concavity	f(x)=2/15x^6-3x^4	$f (x) = \frac{2}{15} x^{6} - 3 x^{4}$
80842	Find the Antiderivative	(x^3)/( square root of 2-x^2)	$\frac{x^{3}}{\sqrt{2 - x^{2}}}$
80843	Evaluate the Integral	integral from 0 to 1 of 1/((1+ square root of x)^4) with respect to x	$\int_{0}^{1} \frac{1}{{(1 + \sqrt{x})}^{4}} d x$
80844	Find the Derivative - d/dx	(x^3)/3- natural log of x	$\frac{x^{3}}{3} - \ln (x)$
80845	Find the Derivative of the Integral	integral from 0 to x^3 of f(t) with respect to t=x^4	$\int_{0}^{x^{3}} f (t) d t = x^{4}$
80846	Evaluate the Integral	integral from 0 to 1 of (x^3+x)(x^4+2x^2+9)^(1/2) with respect to x	$\int_{0}^{1} (x^{3} + x) {(x^{4} + 2 x^{2} + 9)}^{\frac{1}{2}} d x$
80847	Evaluate the Integral	integral of (14x^6+x^2-4x) with respect to x	$\int (14 x^{6} + x^{2} - 4 x) d x$
80848	Find dy/dx	5xy^7-y^3=9x+4y	$5 x y^{7} - y^{3} = 9 x + 4 y$
80849	Find the Antiderivative	x/(x+2)	$\frac{x}{x + 2}$
80850	Find the Antiderivative	1/(x^2-4x+3)	$\frac{1}{x^{2} - 4 x + 3}$
80851	Find the Antiderivative	f(x)=5/(2 square root of 3x+2)+1/(sin(4x)^2)	$f (x) = \frac{5}{2 \sqrt{3 x + 2}} + \frac{1}{\sin^{2} (4 x)}$
80852	Find the Derivative - d/dx	y=(3x+7)/( square root of 5+2x)	$y = \frac{3 x + 7}{\sqrt{5 + 2 x}}$
80853	Find the Antiderivative	tan(x)^5	$\tan^{5} (x)$
80854	Find the Antiderivative	f(x)=tan(x)^2	$f (x) = \tan^{2} (x)$
80855	Evaluate the Integral	integral of 1/(x^4-1) with respect to x	$\int \frac{1}{x^{4} - 1} d x$
80856	Evaluate the Integral	integral of (1/3y)^(1/2) with respect to y	$\int {(\frac{1}{3} y)}^{\frac{1}{2}} d y$
80857	Evaluate the Limit	limit as x approaches infinity of ((x^3+4)^2-x^6)/(x^3)	$lim_{x \to \infty} \frac{{(x^{3} + 4)}^{2} - x^{6}}{x^{3}}$
80858	Find the Antiderivative	f(x)=e^x+x	$f (x) = e^{x} + x$
80859	Find dy/dx	-xy+x^3+5=-y^2	$- x y + x^{3} + 5 = - y^{2}$
80860	Evaluate the Limit	limit as x approaches infinity of square root of (x+2020)*(x+2021)-x	$lim_{x \to \infty} \sqrt{(x + 2020) \cdot (x + 2021)} - x$
80861	Find the Inflection Points	f(x)=3/10x^5-13x^3	$f (x) = \frac{3}{10} x^{5} - 13 x^{3}$
80862	Evaluate the Limit	limit as x approaches 3 of (5x^2-45)/( square root of 5x+1-4)	$lim_{x \to 3} \frac{5 x^{2} - 45}{\sqrt{5 x + 1} - 4}$
80863	Find the Derivative - d/dX	XY^4	$X Y^{4}$
80864	Find the Integral	1/((1+x)^2)	$\frac{1}{{(1 + x)}^{2}}$
80865	Find the Antiderivative	sin(2x)+3cos(3x)	$\sin (2 x) + 3 \cos (3 x)$
80866	Find the Concavity	f(x)=x^2\|x\|	$f (x) = x^{2} \| x \|$
80867	Evaluate the Integral	integral of -5(2(5x^2-5x-1)^2+5(5x^2-5x-1)+2)(2x-1) with respect to x	$\int - 5 (2 {(5 x^{2} - 5 x - 1)}^{2} + 5 (5 x^{2} - 5 x - 1) + 2) (2 x - 1) d x$
80868	Evaluate the Integral	integral from 0 to 1 of 2/( square root of 4-x^2) with respect to x	$\int_{0}^{1} \frac{2}{\sqrt{4 - x^{2}}} d x$
80869	Find the Antiderivative	f(x)=5+x+x^2+x^3	$f (x) = 5 + x + x^{2} + x^{3}$
80870	Find the Inflection Points	f(x)=1/6x^6+x^5+5/3x^4	$f (x) = \frac{1}{6} x^{6} + x^{5} + \frac{5}{3} x^{4}$
80871	Evaluate the Integral	integral of -(4(x^2+x+5)^2+3(x^2+x+5)+4)(2x+1) with respect to x	$\int - (4 {(x^{2} + x + 5)}^{2} + 3 (x^{2} + x + 5) + 4) (2 x + 1) d x$
80872	Find the Derivative - d/dx	y=x^2tanh(2x-1)	$y = x^{2} \tanh (2 x - 1)$
80873	Find the Derivative of the Integral	F(x)=2+ integral from 0 to x of f(t) with respect to t	$F (x) = 2 + \int_{0}^{x} f (t) d t$
80874	Find Where Increasing/Decreasing	f(x)=x^3-3/2x^2-36x	$f (x) = x^{3} - \frac{3}{2} x^{2} - 36 x$
80875	Evaluate the Limit	limit as t approaches 3 of (3-t)/( square root of t+1- square root of 5t-11)	$lim_{t \to 3} \frac{3 - t}{\sqrt{t + 1} - \sqrt{5 t - 11}}$
80876	Evaluate the Limit	limit as x approaches pi of (x+pisec(x))/(x^2-pi^2)	$lim_{x \to π} \frac{x + π \sec (x)}{x^{2} - π^{2}}$
80877	Find the Concavity	f(x)=-1/5x^5-3x^4-12x^3	$f (x) = - \frac{1}{5} x^{5} - 3 x^{4} - 12 x^{3}$
80878	Evaluate the Limit	limit as x approaches infinity of ( natural log of x)^(1/x)	$lim_{x \to \infty} {(\ln (x))}^{\frac{1}{x}}$
80879	Find Where Increasing/Decreasing	j(x)=(2/3x^3-2)^2	$j (x) = {(\frac{2}{3} x^{3} - 2)}^{2}$
80880	Evaluate the Limit	limit as x approaches infinity of 7+1/(3x)-2/(x^2)	$lim_{x \to \infty} 7 + \frac{1}{3 x} - \frac{2}{x^{2}}$
80881	Evaluate Using Summation Formulas	sum from i=1 to n of 6i-5	$\sum_{i = 1}^{n} 6 i - 5$
80882	Find the Integral	tan(x)^4	$\tan^{4} (x)$
80883	Find the Antiderivative	x*e^(x^2+1)	$x \cdot e^{x^{2} + 1}$
80884	Find dy/dx	2y-4x^3=-2y^3	$2 y - 4 x^{3} = - 2 y^{3}$
80885	Evaluate the Integral	integral of x^7cos(x^4) with respect to x	$\int x^{7} \cos (x^{4}) d x$
80886	Find the Antiderivative	f(x)=2/x+3/(x^2)	$f (x) = \frac{2}{x} + \frac{3}{x^{2}}$
80887	Find the Concavity	f(x)=-1/5x^5-x^4	$f (x) = - \frac{1}{5} x^{5} - x^{4}$
80888	Evaluate the Integral	integral of (sin(2x))/(cos(2x)^2) with respect to x	$\int \frac{\sin (2 x)}{\cos^{2} (2 x)} d x$
80889	Evaluate the Limit	limit as x approaches 2 of (2x^3-5x^2+5x-6)/(x-2)	$lim_{x \to 2} \frac{2 x^{3} - 5 x^{2} + 5 x - 6}{x - 2}$
80890	Find the Antiderivative	square root of x^2-1	$\sqrt{x^{2} - 1}$
80891	Evaluate from the Right	limit as x approaches 1 of x^2-2x+4	$lim_{x \to 1} x^{2} - 2 x + 4$
80892	Find the Inflection Points	f(x)=1/12x^4+3x^3+40x^2	$f (x) = \frac{1}{12} x^{4} + 3 x^{3} + 40 x^{2}$
80893	Find the Antiderivative	1/( square root of 1-x square root of 1+x)	$\frac{1}{\sqrt{1 - x} \sqrt{1 + x}}$
80894	Evaluate the Summation	sum from k=0 to 2 of k^4+k^2	$\sum_{k = 0}^{2} k^{4} + k^{2}$
80895	Evaluate the Limit	limit as x approaches pi/2 of 2x+sin(x)	$lim_{x \to \frac{π}{2}} 2 x + \sin (x)$
80896	Evaluate the Limit	limit as x approaches 0 of (2x+sin(3x))/(tan(5x))	$lim_{x \to 0} \frac{2 x + \sin (3 x)}{\tan (5 x)}$
80897	Find the Linearization at g(x)=x³-x²-20x	g(x)=x^3-x^2-20x , x+4	$g (x) = x^{3} - x^{2} - 20 x$ , $x + 4$
80898	Find the Antiderivative	f(x)=5/((2-8x)^3)	$f (x) = \frac{5}{{(2 - 8 x)}^{3}}$
80899	Evaluate the Integral	integral from 0 to 1 of (x^2-1)^4x^3 with respect to x	$\int_{0}^{1} {(x^{2} - 1)}^{4} x^{3} d x$
80900	Integrate By Parts	integral of e^(4theta)sin(5theta) with respect to theta	$\int e^{4 θ} \sin (5 θ) d θ$