Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
80301	Find the Derivative of the Integral	h(x) = integral from 1 to 3x+2 of t/(1+t^3) with respect to t	$h (x) = \int_{1}^{3 x + 2} \frac{t}{1 + t^{3}} d t$
80302	Find the Antiderivative	5e^x-2x^4	$5 e^{x} - 2 x^{4}$
80303	Find the Third Derivative	3x^5+4x^4-18x^2+6x	$3 x^{5} + 4 x^{4} - 18 x^{2} + 6 x$
80304	Find the Derivative - d/dx	y=arctan( square root of x-3)	$y = \arctan (\sqrt{x - 3})$
80305	Evaluate the Integral	integral of 3/(sin(x)^2) with respect to x	$\int \frac{3}{\sin^{2} (x)} d x$
80306	Find the Derivative - d/dx	(d^43)/(dx^43)(sin(2x)+5^(3x))	$\frac{d^{43}}{d x^{43}} (\sin (2 x) + 5^{3 x})$
80307	Evaluate the Integral	integral from 3 to infinity of 1/(x^2-6x+2022) with respect to x	$\int_{3}^{\infty} \frac{1}{x^{2} - 6 x + 2022} d x$
80308	Find the Antiderivative	x/(1+x)	$\frac{x}{1 + x}$
80309	Find the Derivative - d/dx	y=tan(xsin(x))	$y = \tan (x \sin (x))$
80310	Find Where Increasing/Decreasing	f(x) = square root of 2x-5	$f (x) = \sqrt{2 x - 5}$
80311	Find the Inflection Points	f(x)=-2/5x^6+5x^4	$f (x) = - \frac{2}{5} x^{6} + 5 x^{4}$
80312	Find the Antiderivative	1/(x^2)-2/(x^4)	$\frac{1}{x^{2}} - \frac{2}{x^{4}}$
80313	Find the Antiderivative	1/(x square root of x)dx	$\frac{1}{x \sqrt{x}} d x$
80314	Find the Derivative - d/dx	cube root of x-1	$\sqrt[3]{x} - 1$
80315	Find Where Increasing/Decreasing	f(x)=3 cube root of -x-2+6	$f (x) = 3 \sqrt[3]{- x - 2} + 6$
80316	Find the Antiderivative	x square root of 1-x^2	$x \sqrt{1 - x^{2}}$
80317	Evaluate the Limit	limit as x approaches -12 of (8x^3-16x^2-64x)/(x^2+2x)	$lim_{x \to - 12} \frac{8 x^{3} - 16 x^{2} - 64 x}{x^{2} + 2 x}$
80318	Find the Derivative - d/dx	square root of x^3+x^2+x+1	$\sqrt{x^{3} + x^{2} + x + 1}$
80319	Evaluate the Limit	limit as x approaches 2 from the left of square root of 4-2x	$lim_{x \to 2^{-}} \sqrt{4 - 2 x}$
80320	Evaluate the Limit	limit as x approaches infinity of ((3x^2+2x+1)/(x^2-3x+2))^4	$lim_{x \to \infty} {(\frac{3 x^{2} + 2 x + 1}{x^{2} - 3 x + 2})}^{4}$
80321	Find the Derivative Using Quotient Rule - d/dx	y=(4x^2-16)/(x-2)	$y = \frac{4 x^{2} - 16}{x - 2}$
80322	Evaluate the Integral	integral of x^2(5^(x^3)-3^(2x^3)) with respect to x	$\int x^{2} (5^{x^{3}} - 3^{2 x^{3}}) d x$
80323	Evaluate the Integral	integral of ( square root of x square root of x+3/(x^2)) with respect to x	$\int (\sqrt{x} \sqrt{x} + \frac{3}{x^{2}}) d x$
80324	Evaluate the Limit	limit as x approaches -1 of x^4-3x^3+2x^2-5x-7	$lim_{x \to - 1} x^{4} - 3 x^{3} + 2 x^{2} - 5 x - 7$
80325	Evaluate the Integral	integral of -sec(3x)^2 with respect to x	$\int - \sec^{2} (3 x) d x$
80326	Evaluate the Integral	integral of (5x)/(4x+4x^2) with respect to x	$\int \frac{5 x}{4 x + 4 x^{2}} d x$
80327	Find dy/dx	e^y-xy=e	$e^{y} - x y = e$
80328	Evaluate the Limit	limit as x approaches 0 of ( square root of x+4-2)/(x^2+x)	$lim_{x \to 0} \frac{\sqrt{x + 4} - 2}{x^{2} + x}$
80329	Find the Critical Points	a^3y=x^2(2a^2-x^2)	$a^{3} y = x^{2} (2 a^{2} - x^{2})$
80330	Find the Antiderivative	cos(x)^5	$\cos^{5} (x)$
80331	Find the Antiderivative	2sin(x/2)^2	$2 \sin^{2} (\frac{x}{2})$
80332	Find the Antiderivative	f(x)=(2-7x)^4	$f (x) = {(2 - 7 x)}^{4}$
80333	Solve the Differential Equation	x'=3xt^2-3t^2	$x' = 3 x t^{2} - 3 t^{2}$
80334	Evaluate the Integral	integral from 5 to 8 of 1/(x square root of x^2-16) with respect to x	$\int_{5}^{8} \frac{1}{x \sqrt{x^{2} - 16}} d x$
80335	Find the Derivative - d/dx	-4x^-4+sec(x)-e^3	$- 4 x^{- 4} + \sec (x) - e^{3}$
80336	Evaluate Using L'Hospital's Rule	limit as x approaches pi of (x+pisec(x))/(x^2-pi^2)	$lim_{x \to π} \frac{x + π \sec (x)}{x^{2} - π^{2}}$
80337	Evaluate the Integral	integral from -4 to 4 of 3 square root of x with respect to x	$\int_{- 4}^{4} 3 \sqrt{x} d x$
80338	Evaluate the Limit	limit as n approaches infinity of ((n-1)^2-(n+2)^2)/(3-n)	$lim_{n \to \infty} \frac{{(n - 1)}^{2} - {(n + 2)}^{2}}{3 - n}$
80339	Find the Antiderivative	sin(x)+2x	$\sin (x) + 2 x$
80340	Find the Derivative - d/dx	y=arctan( square root of x-9)	$y = \arctan (\sqrt{x - 9})$
80341	Find the Derivative - d/dx	x^(2/3)(20-x)	$x^{\frac{2}{3}} (20 - x)$
80342	Evaluate the Limit	limit as x approaches 0 of (1-cos(x)^2022)/(xsin(x))	$lim_{x \to 0} \frac{1 - \cos^{2022} (x)}{x \sin (x)}$
80343	Find the Second Derivative	e^(e^(x^2))	$e^{e^{x^{2}}}$
80344	Find the Derivative - d/dx	1/2cot(x)	$\frac{1}{2} \cot (x)$
80345	Evaluate the Limit	limit as x approaches 3 from the right of (4e^(2x)+5)/(10-2e^(2x))	$lim_{x \to 3^{+}} \frac{4 e^{2 x} + 5}{10 - 2 e^{2 x}}$
80346	Find the Third Derivative	y=12sin(wt+pi)	$y = 12 \sin (w t + π)$
80347	Evaluate the Integral	integral of (2x^3+2x)u(x) with respect to x=x^6+2x^4+x^2+C	$\int (2 x^{3} + 2 x) u (x) d x = x^{6} + 2 x^{4} + x^{2} + C$
80348	Evaluate the Limit	limit as x approaches 3 of (8x^2+x+3)/(x-4)	$lim_{x \to 3} \frac{8 x^{2} + x + 3}{x - 4}$
80349	Find the Antiderivative	1/(x^(3/2))	$\frac{1}{x^{\frac{3}{2}}}$
80350	Find the Antiderivative	9(2x+1)(x^2+x+1)^8	$9 (2 x + 1) {(x^{2} + x + 1)}^{8}$
80351	Find the Derivative - d/dx	x^2e^(-x^2)	$x^{2} e^{- x^{2}}$
80352	Evaluate the Limit	limit as x approaches -3 of \|x+1\|+3/x	$lim_{x \to - 3} \| x + 1 \| + \frac{3}{x}$
80353	Evaluate the Summation	sum from 6 to 17 of (n-8)/(n+5)	$\sum_{6}^{17} \frac{n - 8}{n + 5}$
80354	Find the Derivative - d/dx	d/(dx)(arcsec(sin(x)))	$\frac{d}{d x} (arcsec (\sin (x)))$
80355	Find the Antiderivative	x*e^(-x)	$x \cdot e^{- x}$
80356	Find the Derivative - d/dx	y=arctan( square root of x-5)	$y = \arctan (\sqrt{x - 5})$
80357	Evaluate the Integral	integral of (5+x)^2 with respect to x	$\int {(5 + x)}^{2} d x$
80358	Evaluate the Integral	integral from -5 to 9 of (2(2x+9)^(1/3))/3 with respect to x	$\int_{- 5}^{9} \frac{2 {(2 x + 9)}^{\frac{1}{3}}}{3} d x$
80359	Find the Second Derivative	y=(5x^2-3)(7x^3+x)	$y = (5 x^{2} - 3) (7 x^{3} + x)$
80360	Find the Antiderivative	x/((x+1)^2)	$\frac{x}{{(x + 1)}^{2}}$
80361	Find the Antiderivative	4e^(-2x)+(x-1)^3	$4 e^{- 2 x} + {(x - 1)}^{3}$
80362	Find the Slope of the Tangent Line at (1/2,16)	f(t)=t^-4 ;, (1/2,16)	$f (t) = t^{- 4}$ ;, $(\frac{1}{2}, 16)$
80363	Find Where Increasing/Decreasing	x^5+10x^4+25x^3	$x^{5} + 10 x^{4} + 25 x^{3}$
80364	Find the Derivative - d/dx	2/3(x-1)^(3/2)	$\frac{2}{3} {(x - 1)}^{\frac{3}{2}}$
80365	Find the Antiderivative	natural log of x^2+1	$\ln (x^{2} + 1)$
80366	Find the Derivative - d/dx	(x^2+5)(3x+1)	$(x^{2} + 5) (3 x + 1)$
80367	Find the Absolute Max and Min over the Interval	f(x)=x^4-8x^2+2 on -3 , 1	$f (x) = x^{4} - 8 x^{2} + 2$ on $- 3$ , $1$
80368	Find the Third Derivative	7x^6-8x^4+5x^2+3	$7 x^{6} - 8 x^{4} + 5 x^{2} + 3$
80369	Find the Derivative - d/dx	y = square root of 4x	$y = \sqrt{4 x}$
80370	Evaluate the Limit	limit as x approaches infinity of 1/x square root of 3+4x^2	$lim_{x \to \infty} \frac{1}{x} \sqrt{3 + 4 x^{2}}$
80371	Find the Maximum/Minimum Value	f(x)=-4 square root of x+5+6	$f (x) = - 4 \sqrt{x + 5} + 6$
80372	Evaluate the Integral	integral of (x+3)(x-2) with respect to x	$\int (x + 3) (x - 2) d x$
80373	Find the Antiderivative	x/( square root of 1+x^2)	$\frac{x}{\sqrt{1 + x^{2}}}$
80374	Find the Absolute Max and Min over the Interval	f(x) = square root of x , 4<=x<=9	$f (x) = \sqrt{x}$ , $4 \leq x \leq 9$
80375	Evaluate the Summation	sum from i=1 to infinity of 1/2(1/3)^(i-1)	$\sum_{i = 1}^{\infty} \frac{1}{2} {(\frac{1}{3})}^{i - 1}$
80376	Evaluate the Limit	limit as h approaches 0 of (3x^4h-5xh^2)/h	$lim_{h \to 0} \frac{3 x^{4} h - 5 x h^{2}}{h}$
80377	Find the Antiderivative	2/x+3/(x^2)	$\frac{2}{x} + \frac{3}{x^{2}}$
80378	Find the Antiderivative	1/(2 square root of 2x+1)	$\frac{1}{2 \sqrt{2 x + 1}}$
80379	Evaluate the Limit	limit as x approaches 4 of -x^3+13x^2-56x+83	$lim_{x \to 4} - x^{3} + 13 x^{2} - 56 x + 83$
80380	Find the Antiderivative	4x natural log of x	$4 x \ln (x)$
80381	Evaluate the Limit	limit as x approaches 2 of square root of (2x^2-5x+7)/(x^2+5)	$lim_{x \to 2} \sqrt{\frac{2 x^{2} - 5 x + 7}{x^{2} + 5}}$
80382	Find the Third Derivative	f(x)=5x^2(x+47)	$f (x) = 5 x^{2} (x + 47)$
80383	Find the Derivative - d/dx	(x^2-3)e^(-x)	$(x^{2} - 3) e^{- x}$
80384	Evaluate the Integral	integral from 0 to 1 of (2x-1)(x+2) with respect to x	$\int_{0}^{1} (2 x - 1) (x + 2) d x$
80385	Evaluate the Integral	integral of 6^(2x)*2 with respect to x	$\int 6^{2 x} \cdot 2 d x$
80386	Find the Percentage Rate of Change	y=350(1+0.75)^t	$y = 350 {(1 + 0.75)}^{t}$
80387	Integrate By Parts	integral of x^3 natural log of (x)^2 with respect to x	$\int x^{3} \ln ({(x)}^{2}) d x$
80388	Find the Antiderivative	(x square root of x+ square root of x)/(x^2)	$\frac{x \sqrt{x} + \sqrt{x}}{x^{2}}$
80389	Find the Derivative of the Integral	integral from 5 to square root of x of f(t) with respect to t=x^2	$\int_{5}^{\sqrt{x}} f (t) d t = x^{2}$
80390	Find dy/dx	y=x^3-2x^2-6x+pi	$y = x^{3} - 2 x^{2} - 6 x + π$
80391	Evaluate the Integral	integral from a to b of 1/(b-a)x with respect to x	$\int_{a}^{b} \frac{1}{b - a} x d x$
80392	Find dy/dx	f(x,y)=x+y+xy	$f (x, y) = x + y + x y$
80393	Find the Slope of the Tangent Line at (1/2,32)	f(t)=t^-5 ;, (1/2,32)	$f (t) = t^{- 5}$ ;, $(\frac{1}{2}, 32)$
80394	Find dy/dx	y=8x^-7+2x^5-5/(x^3)	$y = 8 x^{- 7} + 2 x^{5} - \frac{5}{x^{3}}$
80395	Find the Antiderivative	2xe^x	$2 x e^{x}$
80396	Find the Maximum/Minimum Value	-3cos(6x)	$- 3 \cos (6 x)$
80397	Find the Antiderivative	6e^(2x)+(x+1)^4	$6 e^{2 x} + {(x + 1)}^{4}$
80398	Evaluate the Limit	limit as x approaches 0 of (sin(2x)+5sin(3x))/x	$lim_{x \to 0} \frac{\sin (2 x) + 5 \sin (3 x)}{x}$
80399	Evaluate the Limit	limit as x approaches infinity of (x^2)/( square root of x^2+1)	$lim_{x \to \infty} \frac{x^{2}}{\sqrt{x^{2} + 1}}$
80400	Find the Linearization at θ=0	f(theta)=sin(theta+pi/3) about theta=0	$f (θ) = \sin (θ + \frac{π}{3})$ about $θ = 0$