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Popular Calculus Problems

derivative of y=((sqrt(x))/7+6)^{3/2}	derivative\:y=(\frac{\sqrt{x}}{7}+6)^{\frac{3}{2}}
integral of (2e^x)/(e^{2x)+2e^x+1}	\int\:\frac{2e^{x}}{e^{2x}+2e^{x}+1}dx
derivative of (2x-1/(3x^2))	\frac{d}{dx}(\frac{2x-1}{3x^{2}})
xy^'=y+xe^{y/x}	xy^{\prime\:}=y+xe^{\frac{y}{x}}
area e^{3x},e^x,[0,1]	area\:e^{3x},e^{x},[0,1]
integral from-6 to 8 of 10	\int\:_{-6}^{8}10dx
integral from-4 to 2 of-x^2-2x+8	\int\:_{-4}^{2}-x^{2}-2x+8dx
integral of (2arctan(x))/(x^3)	\int\:\frac{2\arctan(x)}{x^{3}}dx
tangent of y= 2/x ,(7, 2/7)	tangent\:y=\frac{2}{x},(7,\frac{2}{7})
limit as x approaches 0 of x^2(sin(1))/x	\lim\:_{x\to\:0}(x^{2}\frac{\sin(1)}{x})
laplacetransform cos(2t)-sin(2t)	laplacetransform\:\cos(2t)-\sin(2t)
limit as x approaches a/2 of csc(x)	\lim\:_{x\to\:\frac{a}{2}}(\csc(x))
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
derivative of 2e^x+x	derivative\:2e^{x}+x
integral from 3 to infinity of e^{-3x}	\int\:_{3}^{\infty\:}e^{-3x}dx
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))
(\partial)/(\partial x)(e^{yx}*sin(2xy))	\frac{\partial\:}{\partial\:x}(e^{yx}\cdot\:\sin(2xy))
integral from-infinity to 0 of 9^r	\int\:_{-\infty\:}^{0}9^{r}dr
integral of sin(x)+sqrt(36-x^2)	\int\:\sin(x)+\sqrt{36-x^{2}}dx
derivative of (6x/(x+3))	\frac{d}{dx}(\frac{6x}{x+3})
x^6+y^5sqrt(x^7+2)y^'=0	x^{6}+y^{5}\sqrt{x^{7}+2}y^{\prime\:}=0
(\partial)/(\partial x)(x^2y^3z^4)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}z^{4})
derivative of arccot(sqrt(x-1))	\frac{d}{dx}(\arccot(\sqrt{x-1}))
derivative of (9x)/(sqrt(x^2+5))	derivative\:\frac{9x}{\sqrt{x^{2}+5}}
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}})
(d^2y)/(dx^2)+4y=2sin(3x)	\frac{d^{2}y}{dx^{2}}+4y=2\sin(3x)
y^'=k+bcos(2pit)	y^{\prime\:}=k+b\cos(2πt)
derivative of 2x^3+5	\frac{d}{dx}(2x^{3}+5)
derivative of arcsin^2(x)	\frac{d}{dx}(\arcsin^{2}(x))
limit as x approaches 0 of x/(\|x\|)+2	\lim\:_{x\to\:0}(\frac{x}{\left\|x\right\|}+2)
derivative of sin(2θ)	derivative\:\sin(2θ)
integral of (e^{2x}+2e^x+1)/(e^x)	\int\:\frac{e^{2x}+2e^{x}+1}{e^{x}}dx
derivative of csc(4x)	\frac{d}{dx}(\csc(4x))
area y=5x-x^2,y=2x	area\:y=5x-x^{2},y=2x
integral of (5xsqrt(x))/(1+x^5)	\int\:\frac{5x\sqrt{x}}{1+x^{5}}dx
y^{''}-18y^'+145y=0	y^{\prime\:\prime\:}-18y^{\prime\:}+145y=0
tangent of 8sin(x)+6cos(x),\at x=0	tangent\:8\sin(x)+6\cos(x),\at\:x=0
derivative of xsec^2(x+tan(x))	\frac{d}{dx}(x\sec^{2}(x)+\tan(x))
area y=xe^{-0.1x},y=0,x=3	area\:y=xe^{-0.1x},y=0,x=3
integral of cos^3(7-x)sin(7-x)	\int\:\cos^{3}(7-x)\sin(7-x)dx
y^'-x^3=x^3y	y^{\prime\:}-x^{3}=x^{3}y
tangent of f(x)=(sqrt(x))/(x+9),\at x=1	tangent\:f(x)=\frac{\sqrt{x}}{x+9},\at\:x=1
(\partial)/(\partial x)(8e^{xy+5})	\frac{\partial\:}{\partial\:x}(8e^{xy+5})
integral of (x+2)/(x^2+4x+49)	\int\:\frac{x+2}{x^{2}+4x+49}dx
derivative of (12)/(6x^2+1)	derivative\:\frac{12}{6x^{2}+1}
integral of 1/((x^2+4)^{3/2)}	\int\:\frac{1}{(x^{2}+4)^{\frac{3}{2}}}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
area 5ln(x),xln(x)	area\:5\ln(x),x\ln(x)
integral of 1/(3x^2-2x+5)	\int\:\frac{1}{3x^{2}-2x+5}dx
derivative of x^4-8x^2+3	\frac{d}{dx}(x^{4}-8x^{2}+3)
integral of 1/(\sqrt[n]{x)}	\int\:\frac{1}{\sqrt[n]{x}}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})
limit as x approaches 4 of ln(x+2)	\lim\:_{x\to\:4}(\ln(x+2))
integral of x/((x+1)^2(x+2)^2)	\int\:\frac{x}{(x+1)^{2}(x+2)^{2}}dx
(\partial)/(\partial x)(zarctan(y/x))	\frac{\partial\:}{\partial\:x}(z\arctan(\frac{y}{x}))
integral of sin(3x-2)	\int\:\sin(3x-2)dx
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
area y=e^{3x},x=0,x=2	area\:y=e^{3x},x=0,x=2
derivative of-xcos(x-x)	\frac{d}{dx}(-x\cos(x)-x)
derivative of (x^3+7x-1(5x+2))	\frac{d}{dx}((x^{3}+7x-1)(5x+2))
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}
(\partial)/(\partial x)(x^4+x^2y^2+y^5+x+y)	\frac{\partial\:}{\partial\:x}(x^{4}+x^{2}y^{2}+y^{5}+x+y)
laplacetransform 5+e^{-3t}+te^{-4t}	laplacetransform\:5+e^{-3t}+te^{-4t}
integral of 1/((e^{-y)+1)}	\int\:\frac{1}{(e^{-y}+1)}dy
derivative of e^{x^2}+2e^{x^2}x^2	\frac{d}{dx}(e^{x^{2}}+2e^{x^{2}}x^{2})
integral from-4 to 3 of (x^3+x^2-6x)-6x	\int\:_{-4}^{3}(x^{3}+x^{2}-6x)-6xdx
derivative of y= 1/(x^5)	derivative\:y=\frac{1}{x^{5}}
integral of 14	\int\:14dx
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}})
x(dy)/(dx)+y=x^3	x\frac{dy}{dx}+y=x^{3}
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
(dy)/(dx)=2xcos^2(y)	\frac{dy}{dx}=2x\cos^{2}(y)
derivative of (x-4sqrt(1+x)/(x^2-1))	\frac{d}{dx}(\frac{x-4\sqrt{1+x}}{x^{2}-1})
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

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