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Popular Calculus Problems

integral of (1+sin^2(x))/(sqrt(x))	\int\:\frac{1+\sin^{2}(x)}{\sqrt{x}}dx
inverse oflaplace (8s+16)/(s^2+8s+16)	inverselaplace\:\frac{8s+16}{s^{2}+8s+16}
limit as x approaches infinity of (cos(2x))/(x^2)	\lim\:_{x\to\:\infty\:}(\frac{\cos(2x)}{x^{2}})
derivative of 3x-5cos^2(pix)	\frac{d}{dx}(3x-5\cos^{2}(πx))
derivative of 4tan(x^3+2x^2)	derivative\:4\tan(x^{3}+2x^{2})
integral of 1/(x^2+6x+34)	\int\:\frac{1}{x^{2}+6x+34}dx
integral from 1 to 3 of (ln(x))/x	\int\:_{1}^{3}\frac{\ln(x)}{x}dx
slope of (2x+2y)^3=8x^3+8y^3(-1.1)	slope\:(2x+2y)^{3}=8x^{3}+8y^{3}(-1.1)
integral from 1 to 5 of 5/x	\int\:_{1}^{5}\frac{5}{x}dx
derivative of 3/(4x+6)+4x^2	derivative\:\frac{3}{4x+6}+4x^{2}
integral of (20x+7)	\int\:(20x+7)dx
limit as x approaches 2 of (4-x^2)/(x+2)	\lim\:_{x\to\:2}(\frac{4-x^{2}}{x+2})
tangent of f(x)=2x^2+10x+9,\at x=-3	tangent\:f(x)=2x^{2}+10x+9,\at\:x=-3
inverse oflaplace ((s+5))/((s+6)(s+10))	inverselaplace\:\frac{(s+5)}{(s+6)(s+10)}
sum from n=0 to infinity of n/(n^2+4)	\sum\:_{n=0}^{\infty\:}\frac{n}{n^{2}+4}
integral from 0 to 1 of 9	\int\:_{0}^{1}9
integral of 4x^9e^{-x^5}	\int\:4x^{9}e^{-x^{5}}dx
area y=2x,y=5x^2	area\:y=2x,y=5x^{2}
integral of (-4x)	\int\:(-4x)dx
limit as x approaches-6+of (x+5)/(x+6)	\lim\:_{x\to\:-6+}(\frac{x+5}{x+6})
integral of (x^4)/4*1/x	\int\:\frac{x^{4}}{4}\cdot\:\frac{1}{x}dx
y^'=t^2e^{-4t}-4y	y^{\prime\:}=t^{2}e^{-4t}-4y
tangent of f(x)=4x(x^2-4x+5)^7,\at x=2	tangent\:f(x)=4x(x^{2}-4x+5)^{7},\at\:x=2
integral of (x^2-3)^4(2x)	\int\:(x^{2}-3)^{4}(2x)dx
f(x)=e^{4x}	f(x)=e^{4x}
inverse oflaplace s/(s^2+6s+25)	inverselaplace\:\frac{s}{s^{2}+6s+25}
derivative of (3-2x-x^2/(x^2-6))	\frac{d}{dx}(\frac{3-2x-x^{2}}{x^{2}-6})
derivative of x^4+4x^2	\frac{d}{dx}(x^{4}+4x^{2})
integral of-3cos(3x)	\int\:-3\cos(3x)dx
integral of 5^{2x}	\int\:5^{2x}dx
derivative of (ln(2x)^2)	\frac{d}{dx}((\ln(2x))^{2})
integral of (x^2-2x+4)	\int\:(x^{2}-2x+4)dx
(2x^2-ye^x)dx-e^xdy=0	(2x^{2}-ye^{x})dx-e^{x}dy=0
integral of (ln(t))/t	\int\:\frac{\ln(t)}{t}dt
derivative of (1+e^x^{-2})	\frac{d}{dx}((1+e^{x})^{-2})
derivative of \|x^3+10x^2+25x\|	\frac{d}{dx}(\left\|x^{3}+10x^{2}+25x\right\|)
integral from 0 to 1 of x/(sqrt(4-x^2))	\int\:_{0}^{1}\frac{x}{\sqrt{4-x^{2}}}dx
(d^2y)/(dx^2)+2(dy)/(dx)+5y=0	\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}+5y=0
derivative of (sin^2(x)/(cos^2(x)))	\frac{d}{dx}(\frac{\sin^{2}(x)}{\cos^{2}(x)})
integral of x^a	\int\:x^{a}dx
limit as x approaches 3 of-x^2+5x-2	\lim\:_{x\to\:3}(-x^{2}+5x-2)
derivative of arcsin(x^2+y^2-2)	\frac{d}{dx}(\arcsin(x^{2}+y^{2}-2))
integral from 0 to 1 of s^2cos(s^3)	\int\:_{0}^{1}s^{2}\cos(s^{3})ds
implicit (dy)/(dx),2xy=9	implicit\:\frac{dy}{dx},2xy=9
derivative of tan(xcos(x))	\frac{d}{dx}(\tan(x)\cos(x))
derivative of e^{x+1}+4	\frac{d}{dx}(e^{x+1}+4)
(\partial)/(\partial x)(tan(7+2x^2y^4z^2))	\frac{\partial\:}{\partial\:x}(\tan(7+2x^{2}y^{4}z^{2}))
derivative of sqrt(1-e^{cos(1-x^2))}	derivative\:\sqrt{1-e^{\cos(1-x^{2})}}
derivative of f(x)=-2\sqrt[4]{x}	derivative\:f(x)=-2\sqrt[4]{x}
(\partial)/(\partial x)(xy^2z^3-8)	\frac{\partial\:}{\partial\:x}(xy^{2}z^{3}-8)
integral of (6x^2+x+55)/((x+1)(x^2+9))	\int\:\frac{6x^{2}+x+55}{(x+1)(x^{2}+9)}dx
integral of y(1-x^2)	\int\:y(1-x^{2})dy
derivative of (5x-1(6x-3)^{-1})	\frac{d}{dx}((5x-1)(6x-3)^{-1})
derivative of 1+3^x	\frac{d}{dx}(1+3^{x})
derivative of \sqrt[5]{x^3}-7/x	derivative\:\sqrt[5]{x^{3}}-\frac{7}{x}
limit as x approaches 2pi of x	\lim\:_{x\to\:2π}(x)
derivative of sec^2(θ)-3	derivative\:\sec^{2}(θ)-3
derivative of (x^2-4/(x^2+1))	\frac{d}{dx}(\frac{x^{2}-4}{x^{2}+1})
derivative of y=220+65x	derivative\:y=220+65x
derivative of f(x)= x/(x+8)	derivative\:f(x)=\frac{x}{x+8}
(15xy^2-4y)+(15x^2y-4x)y^'=0	(15xy^{2}-4y)+(15x^{2}y-4x)y^{\prime\:}=0
sum from n=1 to infinity of 1/(2^n-1)	\sum\:_{n=1}^{\infty\:}\frac{1}{2^{n}-1}
d/(dt)(-1/(2(t+1) 3/2))	\frac{d}{dt}(-\frac{1}{2(t+1)\frac{3}{2}})
limit as x approaches-2+of (3x-6)/(x+2)	\lim\:_{x\to\:-2+}(\frac{3x-6}{x+2})
derivative of x^3sin(xcos(x))	\frac{d}{dx}(x^{3}\sin(x)\cos(x))
(x^5+y^2)dx-xydy=0	(x^{5}+y^{2})dx-xydy=0
limit as x approaches 7 of 6x+\|x-7\|	\lim\:_{x\to\:7}(6x+\left\|x-7\right\|)
limit as x approaches-5 of x^2-10	\lim\:_{x\to\:-5}(x^{2}-10)
derivative of (8x^3/3)	\frac{d}{dx}(\frac{8x^{3}}{3})
integral of (tan(θ)-1)^2	\int\:(\tan(θ)-1)^{2}dθ
derivative of x^{8/3}	\frac{d}{dx}(x^{\frac{8}{3}})
integral from 1 to infinity of e^{-7x}	\int\:_{1}^{\infty\:}e^{-7x}dx
derivative of acos(x-pi/2+b)	\frac{d}{dx}(a\cos(x-\frac{π}{2})+b)
integral of e^{-t(s+5)}	\int\:e^{-t(s+5)}dt
taylor e^{2x},2	taylor\:e^{2x},2
(\partial)/(\partial z)(e^{xy}ln(z))	\frac{\partial\:}{\partial\:z}(e^{xy}\ln(z))
tangent of f(x)=2x^3+5x^2,\at x=-2	tangent\:f(x)=2x^{3}+5x^{2},\at\:x=-2
derivative of (ax+sqrt(1+x)/(x^2-1))	\frac{d}{dx}(\frac{ax+\sqrt{1+x}}{x^{2}-1})
(\partial)/(\partial x)(2x^2ye^x+2)	\frac{\partial\:}{\partial\:x}(2x^{2}ye^{x}+2)
x(dy)/(dx)+(2x+1)y=e^{-2x}	x\frac{dy}{dx}+(2x+1)y=e^{-2x}
integral of 1/(sqrt(5x^2+20x-10))	\int\:\frac{1}{\sqrt{5x^{2}+20x-10}}dx
limit as x approaches pi/3 of 1/(sec(x))	\lim\:_{x\to\:\frac{π}{3}}(\frac{1}{\sec(x)})
(dy)/(cos(x)+y)=dx	\frac{dy}{\cos(x)+y}=dx
integral from 0 to 1 of sin^2(pix)	\int\:_{0}^{1}\sin^{2}(πx)dx
(\partial)/(\partial x)(arctan(x+2y))	\frac{\partial\:}{\partial\:x}(\arctan(x+2y))
integral of 1/x ln(x^2)	\int\:\frac{1}{x}\ln(x^{2})dx
limit as x approaches 18 of 1/(x-18)	\lim\:_{x\to\:18}(\frac{1}{x-18})
limit as x approaches 1 of f(x)(5-x)	\lim\:_{x\to\:1}(f(x)(5-x))
limit as x approaches 2 of 5x^3-3x+1	\lim\:_{x\to\:2}(5x^{3}-3x+1)
(dy)/(dt)-2ty=6t^2e^{t^2}	\frac{dy}{dt}-2ty=6t^{2}e^{t^{2}}
inverse oflaplace 1/((s^2+4))	inverselaplace\:\frac{1}{(s^{2}+4)}
integral from-2 to 2 of (-x^4)-(x^4-32)	\int\:_{-2}^{2}(-x^{4})-(x^{4}-32)dx
maclaurin 1/(sqrt(1-x^2))	maclaurin\:\frac{1}{\sqrt{1-x^{2}}}
f(x)=(12)/x	f(x)=\frac{12}{x}
(4+x)y^'=5y	(4+x)y^{\prime\:}=5y
integral of (-9)/(\sqrt[3]{x^5)}	\int\:\frac{-9}{\sqrt[3]{x^{5}}}dx
derivative of 1-x^3	\frac{d}{dx}(1-x^{3})
limit as x approaches 0 of (sec(x)tan(x))/x	\lim\:_{x\to\:0}(\frac{\sec(x)\tan(x)}{x})
(dy)/(dx)=(e^y+e^{-y})/(e^x-e^{-x)}	\frac{dy}{dx}=\frac{e^{y}+e^{-y}}{e^{x}-e^{-x}}
integral of (e^{2x}+sin(2x))	\int\:(e^{2x}+\sin(2x))dx

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