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Popular Calculus Problems

integral of 7/(x+1)	\int\:\frac{7}{x+1}dx
integral of 2(sec(x))^2	\int\:2(\sec(x))^{2}dx
(\partial ^2)/(\partial y^2)(y^4sin(6x))	\frac{\partial\:^{2}}{\partial\:y^{2}}(y^{4}\sin(6x))
integral of (2x+7)^{3/2}	\int\:(2x+7)^{\frac{3}{2}}dx
derivative of f(x)= x/5+7/x	derivative\:f(x)=\frac{x}{5}+\frac{7}{x}
derivative of (ax-4sqrt(1+x)/(x^2-1))	\frac{d}{dx}(\frac{ax-4\sqrt{1+x}}{x^{2}-1})
sum from n=1 to infinity of (1/e)^n	\sum\:_{n=1}^{\infty\:}(\frac{1}{e})^{n}
integral of 2/3 x	\int\:\frac{2}{3}xdx
area y=3\sqrt[3]{x},0<= x<= 27	area\:y=3\sqrt[3]{x},0\le\:x\le\:27
(\partial)/(\partial x)(sqrt(1+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{1+x^{2}+y^{2}})
integral from 1-2x to 1+2x of tsin(t)	\int\:_{1-2x}^{1+2x}t\sin(t)dt
derivative of x/(sqrt(x^2+16))	\frac{d}{dx}(\frac{x}{\sqrt{x^{2}+16}})
derivative of 7sin(3x)	\frac{d}{dx}(7\sin(3x))
integral of (x^2-9x+4)	\int\:(x^{2}-9x+4)dx
integral of (3x^2)/(sqrt(5x^3+1))	\int\:\frac{3x^{2}}{\sqrt{5x^{3}+1}}dx
4y^{''}-y=xe^{x/2}	4y^{\prime\:\prime\:}-y=xe^{\frac{x}{2}}
integral of 5x^4-3x^2+7	\int\:5x^{4}-3x^{2}+7dx
limit as x approaches-2.4 of x	\lim\:_{x\to\:-2.4}(x)
y^'=(2y)/(3x),y(27)=4	y^{\prime\:}=\frac{2y}{3x},y(27)=4
integral of x/((x+4)(2x-1))	\int\:\frac{x}{(x+4)(2x-1)}dx
integral of 8x-1	\int\:8x-1dx
maclaurin xcos(x^3)	maclaurin\:x\cos(x^{3})
derivative of (sqrt(x)/((9+x)))	\frac{d}{dx}(\frac{\sqrt{x}}{(9+x)})
derivative of (6^x+5/(6^x+2))	\frac{d}{dx}(\frac{6^{x}+5}{6^{x}+2})
integral of sin(y)sin(x)	\int\:\sin(y)\sin(x)dy
integral of e^{ln(x+2)}	\int\:e^{\ln(x+2)}dx
y^{''}+1.9*y^'=0,y(0)=0,y^'(0)=1	y^{\prime\:\prime\:}+1.9\cdot\:y^{\prime\:}=0,y(0)=0,y^{\prime\:}(0)=1
integral of x/(x^2+x-1)	\int\:\frac{x}{x^{2}+x-1}dx
derivative of sec(8x^3+1)	\frac{d}{dx}(\sec(8x^{3}+1))
tangent of f(x)=18sqrt(x),\at x=9	tangent\:f(x)=18\sqrt{x},\at\:x=9
sum from n=2 to infinity of 7/(4^n)	\sum\:_{n=2}^{\infty\:}\frac{7}{4^{n}}
limit as x approaches infinity of e^xx	\lim\:_{x\to\:\infty\:}(e^{x}x)
integral of 3/(x+4)	\int\:\frac{3}{x+4}dx
limit as x approaches 4 of (2x-3)^2	\lim\:_{x\to\:4}((2x-3)^{2})
integral from 0 to 2 of 1/(x^2-4)	\int\:_{0}^{2}\frac{1}{x^{2}-4}dx
derivative of (2+x^{-3})	\frac{d}{dx}((2+x)^{-3})
integral of θ^2sin(2θ)	\int\:θ^{2}\sin(2θ)dθ
integral of e^{-st}t^3	\int\:e^{-st}t^{3}dt
derivative of (sin(x)dx)	\frac{d}{dx}((\sin(x))dx)
limit as x approaches 2 of (x-1)/(x-2)	\lim\:_{x\to\:2}(\frac{x-1}{x-2})
limit as x approaches 0+of cos^{1/x}(x)	\lim\:_{x\to\:0+}(\cos^{\frac{1}{x}}(x))
(\partial)/(\partial x)(y^5-3xy)	\frac{\partial\:}{\partial\:x}(y^{5}-3xy)
x^{''}+4x^'+4x=0	x^{\prime\:\prime\:}+4x^{\prime\:}+4x=0
derivative of (60t+180)/(t+6)	derivative\:\frac{60t+180}{t+6}
integral from 2 to 3 of x/(x^2+1)	\int\:_{2}^{3}\frac{x}{x^{2}+1}dx
derivative of xln(y)	\frac{d}{dx}(x\ln(y))
integral of-4/3	\int\:-\frac{4}{3}
(\partial)/(\partial x)(2xy+y)	\frac{\partial\:}{\partial\:x}(2xy+y)
integral from 0 to 1 of (x-sqrt(x))/7	\int\:_{0}^{1}\frac{x-\sqrt{x}}{7}dx
integral of 2ln(x)x	\int\:2\ln(x)xdx
integral from 0 to 16 of 4sqrt(x)-x	\int\:_{0}^{16}4\sqrt{x}-xdx
(\partial}{\partial y}(\frac{8.31x)/y)	\frac{\partial\:}{\partial\:y}(\frac{8.31x}{y})
x^'=x^2	x^{\prime\:}=x^{2}
laplacetransform e^{2t}cos(3t+5)	laplacetransform\:e^{2t}\cos(3t+5)
maclaurin 1/(4+x)	maclaurin\:\frac{1}{4+x}
limit as z approaches 0 of 8/(z^3)+5/z+2	\lim\:_{z\to\:0}(\frac{8}{z^{3}}+\frac{5}{z}+2)
derivative of x^5-2x^3+x	\frac{d}{dx}(x^{5}-2x^{3}+x)
integral of (x+3)sqrt(6x+x^2)	\int\:(x+3)\sqrt{6x+x^{2}}dx
d/(dt)(sqrt(1-t))	\frac{d}{dt}(\sqrt{1-t})
implicit (dy)/(dx),y=((x^2+2x))/(4-5x)	implicit\:\frac{dy}{dx},y=\frac{(x^{2}+2x)}{4-5x}
derivative of 1/(4x^{3/4})	\frac{d}{dx}(\frac{1}{4x^{\frac{3}{4}}})
(\partial)/(\partial x)(1.85+2.05x+0.656y)	\frac{\partial\:}{\partial\:x}(1.85+2.05x+0.656y)
integral of sin^4(x)+cos^4(x)	\int\:\sin^{4}(x)+\cos^{4}(x)dx
area sqrt(x),y=x-2,y=0	area\:\sqrt{x},y=x-2,y=0
limit as x approaches 4 of ln(e^x)	\lim\:_{x\to\:4}(\ln(e^{x}))
limit as x approaches 0 of sin(1x)	\lim\:_{x\to\:0}(\sin(1x))
sum from n=1 to infinity}e^{-sqrt(n of)	\sum\:_{n=1}^{\infty\:}e^{-\sqrt{n}}
derivative of 1/(x^4*(5-x))	\frac{d}{dx}(\frac{1}{x^{4}\cdot\:(5-x)})
derivative of (x^2+x-2/(x-2))	\frac{d}{dx}(\frac{x^{2}+x-2}{x-2})
(\partial)/(\partial x)(ln(x^6-y^4))	\frac{\partial\:}{\partial\:x}(\ln(x^{6}-y^{4}))
tangent of f(x)=2(x-3)^2+1,(4,3)	tangent\:f(x)=2(x-3)^{2}+1,(4,3)
d/(dt)(cos((t^3)/(10)))	\frac{d}{dt}(\cos(\frac{t^{3}}{10}))
limit as x approaches 2 of (9x)/(x-2)	\lim\:_{x\to\:2}(\frac{9x}{x-2})
integral of x^2*3^{2x}	\int\:x^{2}\cdot\:3^{2x}dx
sum from n=1 to infinity of 1/(n^{0.7)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{0.7}}
integral of 1/(sqrt(-7-8x-x^2))	\int\:\frac{1}{\sqrt{-7-8x-x^{2}}}dx
derivative of ln(x+ln(y))	\frac{d}{dx}(\ln(x)+\ln(y))
(\partial)/(\partial x)(y^2zln(1+x^2))	\frac{\partial\:}{\partial\:x}(y^{2}z\ln(1+x^{2}))
derivative of y=cos^{ln(7x)}(x)	derivative\:y=\cos^{\ln(7x)}(x)
integral of 1/(sin(x)-cos(x)-1)	\int\:\frac{1}{\sin(x)-\cos(x)-1}dx
integral from 0 to 7/3 of sqrt(9+3x)	\int\:_{0}^{\frac{7}{3}}\sqrt{9+3x}dx
(\partial)/(\partial x)(log_{e}(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\log_{e}(x^{2}+y^{2}))
integral of ((5t-t))/(sqrt(3t^2-9))	\int\:\frac{(5t-t)}{\sqrt{3t^{2}-9}}dt
(\partial)/(\partial x)(x^4-3x^2y^2+y^4)	\frac{\partial\:}{\partial\:x}(x^{4}-3x^{2}y^{2}+y^{4})
limit as x approaches-2 of sqrt(4^2-3)	\lim\:_{x\to\:-2}(\sqrt{4^{2}-3})
y^{''}-y^'-2y=0,y(0)=0,y(pi/2)=1	y^{\prime\:\prime\:}-y^{\prime\:}-2y=0,y(0)=0,y(\frac{π}{2})=1
derivative of f(x)=4x^2-1	derivative\:f(x)=4x^{2}-1
tangent of y=(1+5x)^{12},(0,1)	tangent\:y=(1+5x)^{12},(0,1)
xy^'+2y=2e^x	xy^{\prime\:}+2y=2e^{x}
(dx)/(dt)=sin(x)	\frac{dx}{dt}=\sin(x)
integral of e^{x/(16)}	\int\:e^{\frac{x}{16}}dx
integral of x^2(x-7)	\int\:x^{2}(x-7)dx
integral of x(2x^2+1)^6	\int\:x(2x^{2}+1)^{6}dx
derivative of t+1	derivative\:t+1
derivative of \sqrt[3]{2x-1}	\frac{d}{dx}(\sqrt[3]{2x-1})
derivative of (2x/(x+9))	\frac{d}{dx}(\frac{2x}{x+9})
(\partial)/(\partial x)(8-x^2+xy-4y^2)	\frac{\partial\:}{\partial\:x}(8-x^{2}+xy-4y^{2})
integral of (ln(x))/(e^x)	\int\:\frac{\ln(x)}{e^{x}}dx
derivative of f(x)=x^2+2x+1	derivative\:f(x)=x^{2}+2x+1
sum from n=1 to infinity of (x^n)/(8^n)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{8^{n}}

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