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Popular Calculus Problems

tangent of y=sin(7x)+sin^2(7x),(0,0)	tangent\:y=\sin(7x)+\sin^{2}(7x),(0,0)
integral from 0 to 1 of \|2x-1\|	\int\:_{0}^{1}\left\|2x-1\right\|dx
integral from 0 to 2pi of cos(3t)e^{-2t}	\int\:_{0}^{2π}\cos(3t)e^{-2t}dt
y^{''}-2y^'+82y=0	y^{\prime\:\prime\:}-2y^{\prime\:}+82y=0
limit as x approaches 0+of (1+sqrt(x))^x	\lim\:_{x\to\:0+}((1+\sqrt{x})^{x})
limit as x approaches 0+of tan(5x)ln(8x)	\lim\:_{x\to\:0+}(\tan(5x)\ln(8x))
area y=4x^2,y=2\sqrt[3]{4}	area\:y=4x^{2},y=2\sqrt[3]{4}
limit as x approaches 1/4 of tan(pix)	\lim\:_{x\to\:\frac{1}{4}}(\tan(πx))
derivative of (6x/(x+3))	\frac{d}{dx}(\frac{6x}{x+3})
derivative of arccot(sqrt(x-1))	\frac{d}{dx}(\arccot(\sqrt{x-1}))
limit as x approaches pi/2 of (tan(2x))/(x-pi/2)	\lim\:_{x\to\:\frac{π}{2}}(\frac{\tan(2x)}{x-\frac{π}{2}})
derivative of arcsin^2(x)	\frac{d}{dx}(\arcsin^{2}(x))
derivative of sin(2θ)	derivative\:\sin(2θ)
derivative of csc(4x)	\frac{d}{dx}(\csc(4x))
y^{''}-18y^'+145y=0	y^{\prime\:\prime\:}-18y^{\prime\:}+145y=0
integral of cos^3(7-x)sin(7-x)	\int\:\cos^{3}(7-x)\sin(7-x)dx
integral from 0 to 4 of 6x-x^2	\int\:_{0}^{4}6x-x^{2}dx
(dy)/(dx)=(x-5)e^{-2y},y(5)=ln(5)	\frac{dy}{dx}=(x-5)e^{-2y},y(5)=\ln(5)
integral of (3x^2)/(sqrt(49-x^2))	\int\:\frac{3x^{2}}{\sqrt{49-x^{2}}}dx
integral of (e^y)/((e^y+1)^2)	\int\:\frac{e^{y}}{(e^{y}+1)^{2}}dy
y^'=(y*e^x)/x	y^{\prime\:}=\frac{y\cdot\:e^{x}}{x}
integral from 3 to 4 of x/(x^2+4x+20)	\int\:_{3}^{4}\frac{x}{x^{2}+4x+20}dx
derivative of (4x^2-2x^4)	\frac{d}{dx}((4x^{2}-2x)^{4})
limit as t approaches 0 of (e^{6t}-1)/(sin(t))	\lim\:_{t\to\:0}(\frac{e^{6t}-1}{\sin(t)})
limit as θ approaches+0 of (sin(8θ))/θ	\lim\:_{θ\to\:+0}(\frac{\sin(8θ)}{θ})
integral of e^{-9x}	\int\:e^{-9x}dx
integral of 1/(3x^2-2x+5)	\int\:\frac{1}{3x^{2}-2x+5}dx
x^3y^'+x^2y=x^7y^{3/4}	x^{3}y^{\prime\:}+x^{2}y=x^{7}y^{\frac{3}{4}}
derivative of-7e^{-7x}	\frac{d}{dx}(-7e^{-7x})
(\partial)/(\partial x)(zarctan(y/x))	\frac{\partial\:}{\partial\:x}(z\arctan(\frac{y}{x}))
derivative of x^2+3x+4	derivative\:x^{2}+3x+4
integral of xsqrt(x+8)	\int\:x\sqrt{x+8}dx
integral of 0.0018h^2	\int\:0.0018h^{2}dh
derivative of-xcos(x-x)	\frac{d}{dx}(-x\cos(x)-x)
limit as x approaches 1 of 0/0	\lim\:_{x\to\:1}(\frac{0}{0})
derivative of f(x)=sqrt(x^2-4x+3)	derivative\:f(x)=\sqrt{x^{2}-4x+3}
integral of 2pix^3sin(x)	\int\:2πx^{3}\sin(x)dx
(\partial)/(\partial x)((y^3)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{y^{3}}{x^{2}+y^{2}})
derivative of f(x)=ccos(t)+t^2sin(t)	derivative\:f(x)=c\cos(t)+t^{2}\sin(t)
integral from 3 to 4 of (x+7x^2)	\int\:_{3}^{4}(x+7x^{2})dx
derivative of ln(3)*e^x	derivative\:\ln(3)\cdot\:e^{x}
integral of x^3sin(x	\int\:x^{3}\sin(d)xdx
integral of 34.7x	\int\:34.7xdx
integral of (x+5)/(x^2+25)	\int\:\frac{x+5}{x^{2}+25}dx
integral of (9x^2-8x+24)/(x^3+4x)	\int\:\frac{9x^{2}-8x+24}{x^{3}+4x}dx
xy^'-y=x^2+2x+1	xy^{\prime\:}-y=x^{2}+2x+1
integral of x^3(4x^2+5)	\int\:x^{3}(4x^{2}+5)dx
inverse oflaplace (6(s+34))/(s(s^2+10s+34))	inverselaplace\:\frac{6(s+34)}{s(s^{2}+10s+34)}
normal of f(x)=x^4+5e^x,(0,5)	normal\:f(x)=x^{4}+5e^{x},(0,5)
derivative of f(x)=ax	derivative\:f(x)=ax
integral from-infinity to 0 of x*e^x	\int\:_{-\infty\:}^{0}x\cdot\:e^{x}dx
(dx)/(dt)=x^2e^{-2t}	\frac{dx}{dt}=x^{2}e^{-2t}
integral of ((3-x)/(sqrt(x^2-6x+2)))	\int\:(\frac{3-x}{\sqrt{x^{2}-6x+2}})dx
derivative of cos((pix/4))	\frac{d}{dx}(\cos(\frac{πx}{4}))
tangent of f(x)=x^2,\at x=-3	tangent\:f(x)=x^{2},\at\:x=-3
limit as x approaches 4 of (x^{q(x)}(4-x))/(e^{4-x)-1}	\lim\:_{x\to\:4}(\frac{x^{q(x)}(4-x)}{e^{4-x}-1})
limit as x approaches 9 of 7/(x-9)	\lim\:_{x\to\:9}(\frac{7}{x-9})
integral of x^3-6x	\int\:x^{3}-6xdx
(x^4e^{-x})^'	(x^{4}e^{-x})^{\prime\:}
(\partial)/(\partial x)(4x-3x^4y^2)	\frac{\partial\:}{\partial\:x}(4x-3x^{4}y^{2})
integral of (t^5)/(sqrt(t^2+2))	\int\:\frac{t^{5}}{\sqrt{t^{2}+2}}dt
integral of 1/(y^{3/2)}	\int\:\frac{1}{y^{\frac{3}{2}}}dy
(\partial)/(\partial x)(e^xxy+e^xy^2)	\frac{\partial\:}{\partial\:x}(e^{x}xy+e^{x}y^{2})
((2x+y+1)dy)/(dx)=1	\frac{(2x+y+1)dy}{dx}=1
d/(dz)((az^2)/(a^2+z^2))	\frac{d}{dz}(\frac{az^{2}}{a^{2}+z^{2}})
integral of x^3sqrt(x^2-7)	\int\:x^{3}\sqrt{x^{2}-7}dx
integral of 1/(x^3sqrt(9x^2-1))	\int\:\frac{1}{x^{3}\sqrt{9x^{2}-1}}dx
2y^{''}+3y^'-4y=5e^{3x}	2y^{\prime\:\prime\:}+3y^{\prime\:}-4y=5e^{3x}
sum from n=1 to infinity of ((3x-2)^n)/n	\sum\:_{n=1}^{\infty\:}\frac{(3x-2)^{n}}{n}
sum from n=1 to infinity of (7n)/(5n+1)	\sum\:_{n=1}^{\infty\:}\frac{7n}{5n+1}
integral of 20xsec^2(x)	\int\:20x\sec^{2}(x)dx
integral of 1/(x*sqrt(x-1))	\int\:\frac{1}{x\cdot\:\sqrt{x-1}}dx
(\partial)/(\partial x)(sqrt((x+4)/(y+4)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{x+4}{y+4}})
integral of 1/(2-cos(x))	\int\:\frac{1}{2-\cos(x)}dx
(\partial)/(\partial x)(2x+2y)	\frac{\partial\:}{\partial\:x}(2x+2y)
(\partial)/(\partial x)(9x+y+7xy)	\frac{\partial\:}{\partial\:x}(9x+y+7xy)
f^'(x)=sqrt(1-2x)	f^{\prime\:}(x)=\sqrt{1-2x}
limit as x approaches infinity of x^2+5x	\lim\:_{x\to\:\infty\:}(x^{2}+5x)
derivative of (e^{t/2}-e)^{-1/3}	derivative\:(e^{\frac{t}{2}}-e)^{-\frac{1}{3}}
(\partial)/(\partial x)((e^y)/(x+y^4))	\frac{\partial\:}{\partial\:x}(\frac{e^{y}}{x+y^{4}})
derivative of y=-6x^5+2	derivative\:y=-6x^{5}+2
derivative of x/(e^x-1)	derivative\:\frac{x}{e^{x}-1}
integral of (sin(inx))/x	\int\:\frac{\sin(inx)}{x}dx
integral of 8cos(3x)	\int\:8\cos(3x)dx
derivative of 1/12 (e^{6x}+e^{-6x})	\frac{d}{dx}(\frac{1}{12}(e^{6x}+e^{-6x}))
integral of (12)/((1+x+y)^5)	\int\:\frac{12}{(1+x+y)^{5}}dy
x^2y^'+x(x+2)y=ex	x^{2}y^{\prime\:}+x(x+2)y=ex
(dy)/(dx)+1/x y=2	\frac{dy}{dx}+\frac{1}{x}y=2
integral of 5cos(t)	\int\:5\cos(t)dt
derivative of f(x)=(4x-2x^3)(4+sqrt(x))	derivative\:f(x)=(4x-2x^{3})(4+\sqrt{x})
slope of (-3,9),(2,-1)	slope\:(-3,9),(2,-1)
derivative of 1/(x*sqrt(x))	\frac{d}{dx}(\frac{1}{x\cdot\:\sqrt{x}})
integral of 2t^3	\int\:2t^{3}dt
integral of 2/(xsqrt(x^2+1))	\int\:\frac{2}{x\sqrt{x^{2}+1}}dx
integral of e^{6x}sin(6x)	\int\:e^{6x}\sin(6x)dx
(dy)/(dx)-y^2=0	\frac{dy}{dx}-y^{2}=0
derivative of (x^4/(2-x^3))	\frac{d}{dx}(\frac{x^{4}}{2-x^{3}})
integral of 216sin(6x)\sqrt[3]{cos(6x)}	\int\:216\sin(6x)\sqrt[3]{\cos(6x)}dx
derivative of csc(x(x+cot(x)))	\frac{d}{dx}(\csc(x)(x+\cot(x)))
derivative of 2sin(x^2)	derivative\:2\sin(x^{2})

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