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Popular Calculus Problems

integral of (13)/(x^2+1)	\int\:\frac{13}{x^{2}+1}dx
(dy)/(dx)=sqrt(3y)e^{x+8}	\frac{dy}{dx}=\sqrt{3y}e^{x+8}
limit as x approaches infinity of (-1)^x*(1-1/(x^2))	\lim\:_{x\to\:\infty\:}((-1)^{x}\cdot\:(1-\frac{1}{x^{2}}))
integral of sin^2(φ)	\int\:\sin^{2}(φ)dφ
derivative of f(x)=4x^{(2)}(x-3)	derivative\:f(x)=4x^{(2)}(x-3)
limit as x approaches infinity of x^2+2x	\lim\:_{x\to\:\infty\:}(x^{2}+2x)
derivative of arctan(8/x)	\frac{d}{dx}(\arctan(\frac{8}{x}))
integral of 4/((x+3)^2)	\int\:\frac{4}{(x+3)^{2}}dx
(\partial)/(\partial y)(x^3y^{10}sin(xy^2))	\frac{\partial\:}{\partial\:y}(x^{3}y^{10}\sin(xy^{2}))
integral of 6te^{3t}	\int\:6te^{3t}dt
limit as x approaches 0 of (\|x^3\|)/(x^3)	\lim\:_{x\to\:0}(\frac{\left\|x^{3}\right\|}{x^{3}})
derivative of a^2sin^2(x)	\frac{d}{dx}(a^{2}\sin^{2}(x))
tangent of f(x)= x/(x+3),\at x=-2	tangent\:f(x)=\frac{x}{x+3},\at\:x=-2
limit as t approaches+0 of (sin(2t))/t	\lim\:_{t\to\:+0}(\frac{\sin(2t)}{t})
derivative of ((s+2))/((s^2+4s+13))	derivative\:\frac{(s+2)}{(s^{2}+4s+13)}
t^2(dx)/(dt)+3tx=t^4log_{10}(t)+1	t^{2}\frac{dx}{dt}+3tx=t^{4}\log_{10}(t)+1
derivative of 1/(x+xln(x))	derivative\:\frac{1}{x+x\ln(x)}
derivative of f(x)=(4x^2+3)(4x-5)	derivative\:f(x)=(4x^{2}+3)(4x-5)
derivative of ln(25)	\frac{d}{dx}(\ln(25))
limit as x approaches 0 of ((8^x-1))/x	\lim\:_{x\to\:0}(\frac{(8^{x}-1)}{x})
integral of 1 (x)	\int\:\frac{d}{1}(x)dx
integral from-3 to 6 of sqrt(3+x)	\int\:_{-3}^{6}\sqrt{3+x}dx
(\partial)/(\partial x)(e^{9z})	\frac{\partial\:}{\partial\:x}(e^{9z})
limit as x approaches 0 of 1+x^2	\lim\:_{x\to\:0}(1+x^{2})
integral of (e^y)	\int\:(e^{y})dy
area sqrt(1+3x),1<= x<= 3	area\:\sqrt{1+3x},1\le\:x\le\:3
integral from 0 to 16 of 1/2 x	\int\:_{0}^{16}\frac{1}{2}xdx
integral of (ln(14x))/x	\int\:\frac{\ln(14x)}{x}dx
integral from 0 to 3 of 2pi(x)(2x)	\int\:_{0}^{3}2π(x)(2x)dx
derivative of e^x(x^2-2x+2)	\frac{d}{dx}(e^{x}(x^{2}-2x+2))
integral of e^ssin(1-s)	\int\:e^{s}\sin(1-s)ds
derivative of 5cos((pi/4 x)+pi/4)	derivative\:5\cos((\frac{π}{4}x)+\frac{π}{4})
derivative of sqrt(3x^2+y^2-1)	\frac{d}{dx}(\sqrt{3x^{2}+y^{2}-1})
integral from 0 to 1 of (x-x^4)	\int\:_{0}^{1}(x-x^{4})dx
area y=3x,y=7x^2	area\:y=3x,y=7x^{2}
derivative of f(x(4x^2-2))	\frac{d}{dx}(f(x)(4x^{2}-2))
derivative of (2x/(5-tan(x)))	\frac{d}{dx}(\frac{2x}{5-\tan(x)})
derivative of (2x+5/(3x-1))	\frac{d}{dx}(\frac{2x+5}{3x-1})
integral of (6x^5-4x^3+1/(sqrt(x)))	\int\:(6x^{5}-4x^{3}+\frac{1}{\sqrt{x}})dx
derivative of 4e(cos(x)-xsin(x))	derivative\:4e(\cos(x)-x\sin(x))
limit as x approaches 4 of 6/(x-4)	\lim\:_{x\to\:4}(\frac{6}{x-4})
limit as x approaches 3 of 2x+\|x+3\|	\lim\:_{x\to\:3}(2x+\left\|x+3\right\|)
integral of 8/9 x^{8/9}	\int\:\frac{8}{9}x^{\frac{8}{9}}dx
d/(dy)((e^x)/y)	\frac{d}{dy}(\frac{e^{x}}{y})
integral of 3/(xln^2(3x))	\int\:\frac{3}{x\ln^{2}(3x)}dx
(\partial)/(\partial x)(x*e^{xy+1})	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{xy+1})
limit as x approaches infinity of (cos(21x))/(21x)	\lim\:_{x\to\:\infty\:}(\frac{\cos(21x)}{21x})
derivative of 2/5 x	\frac{d}{dx}(\frac{2}{5}x)
(dy)/(dx)=3x^4-6x^3+3x-8	\frac{dy}{dx}=3x^{4}-6x^{3}+3x-8
tangent of f(x)=5x^3-5x^2+2,(1,2)	tangent\:f(x)=5x^{3}-5x^{2}+2,(1,2)
limit as x approaches-1-of sqrt(3x+3)-5	\lim\:_{x\to\:-1-}(\sqrt{3x+3}-5)
y^'=((y-y^2))/t	y^{\prime\:}=\frac{(y-y^{2})}{t}
derivative of 5\sqrt[5]{x}	derivative\:5\sqrt[5]{x}
inverse oflaplace 1/(s-5)	inverselaplace\:\frac{1}{s-5}
y^'+6y=60,y(1)=110	y^{\prime\:}+6y=60,y(1)=110
y^'=19sqrt(x)y	y^{\prime\:}=19\sqrt{x}y
inverse oflaplace (s^2)/(s^3+2*s^2-1)	inverselaplace\:\frac{s^{2}}{s^{3}+2\cdot\:s^{2}-1}
integral from 0 to 7 of (6t)/((t-8)^2)	\int\:_{0}^{7}\frac{6t}{(t-8)^{2}}dt
derivative of (x^2+1^{x+1})	\frac{d}{dx}((x^{2}+1)^{x+1})
sum from n=0 to infinity of n(3/4)^n	\sum\:_{n=0}^{\infty\:}n(\frac{3}{4})^{n}
(\partial)/(\partial y)((-y)/((x^2+y^2)))	\frac{\partial\:}{\partial\:y}(\frac{-y}{(x^{2}+y^{2})})
(ln(x+1))^2-e^{x^2}	(\ln(x+1))^{2}-e^{x^{2}}
integral of ((z+2))/(z^2+3z-1)	\int\:\frac{(z+2)}{z^{2}+3z-1}dz
integral of tsin(pit)	\int\:t\sin(πt)dt
(\partial)/(\partial x)(5(y+3)^3(x-4))	\frac{\partial\:}{\partial\:x}(5\cdot\:(y+3)^{3}\cdot\:(x-4))
derivative of f(x)=(x^2+2)^2	derivative\:f(x)=(x^{2}+2)^{2}
derivative of f(x)=(8x^3+3x^2)^3	derivative\:f(x)=(8x^{3}+3x^{2})^{3}
(\partial)/(\partial x)(2xy-2x^2y)	\frac{\partial\:}{\partial\:x}(2xy-2x^{2}y)
limit as x approaches infinity of ln(5x)	\lim\:_{x\to\:\infty\:}(\ln(5x))
integral of xsqrt(x-27)	\int\:x\sqrt{x-27}dx
derivative of 3/(sqrt(x+8))	\frac{d}{dx}(\frac{3}{\sqrt{x+8}})
inverse oflaplace (3x)/((x-1)^4)	inverselaplace\:\frac{3x}{(x-1)^{4}}
derivative of arctan(x^2+y^2)	\frac{d}{dx}(\arctan(x^{2}+y^{2}))
d/(dy)(y-1)	\frac{d}{dy}(y-1)
integral of (1/(cos(x)))	\int\:(\frac{1}{\cos(x)})dx
tangent of 6-5x^2	tangent\:6-5x^{2}
sum from n=1 to infinity of 5/(n^2+9)	\sum\:_{n=1}^{\infty\:}\frac{5}{n^{2}+9}
integral from 1/5 to 3 of 6xln(5x)	\int\:_{\frac{1}{5}}^{3}6x\ln(5x)dx
partialfraction (2x)/(x-1)	partialfraction\:\frac{2x}{x-1}
y^'= 1/((t-1)(y+1)),y(0)=1	y^{\prime\:}=\frac{1}{(t-1)(y+1)},y(0)=1
integral of 1/(s^2-2s+5)	\int\:\frac{1}{s^{2}-2s+5}ds
limit as x approaches-4 of (4-\|x\|)/(4+x)	\lim\:_{x\to\:-4}(\frac{4-\left\|x\right\|}{4+x})
derivative of csecx	\frac{d}{dx}(csecx)
(\partial)/(\partial x)(sqrt(5-x^2+3y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{5-x^{2}+3y^{2}})
tangent of 3x^2,\at x=2	tangent\:3x^{2},\at\:x=2
limit as x approaches 0 of (sqrt(1+x))/x	\lim\:_{x\to\:0}(\frac{\sqrt{1+x}}{x})
y^{''}=e^{-x}	y^{\prime\:\prime\:}=e^{-x}
integral of cos(xt)	\int\:\cos(xt)dt
integral of 1/8	\int\:\frac{1}{8}dx
integral of (sqrt(x))/(1+\sqrt[4]{x^3)}	\int\:\frac{\sqrt{x}}{1+\sqrt[4]{x^{3}}}dx
integral from 2 to infinity of e^{-4x}	\int\:_{2}^{\infty\:}e^{-4x}dx
(\partial)/(\partial x)(xye^{x^2+y^2})	\frac{\partial\:}{\partial\:x}(xye^{x^{2}+y^{2}})
integral of (2cos(x))/(sin^2(x)+sin(x))	\int\:\frac{2\cos(x)}{\sin^{2}(x)+\sin(x)}dx
limit as x approaches 1 of x/(x^2+2)	\lim\:_{x\to\:1}(\frac{x}{x^{2}+2})
derivative of f(x)=(3pix^2)/2	derivative\:f(x)=\frac{3πx^{2}}{2}
integral of (1+x)/(sqrt(1-x^2))	\int\:\frac{1+x}{\sqrt{1-x^{2}}}dx
tangent of 2/(3x+1)	tangent\:\frac{2}{3x+1}
(\partial)/(\partial y)(2-sqrt(y-x^2))	\frac{\partial\:}{\partial\:y}(2-\sqrt{y-x^{2}})
derivative of x^5e^{3x}	\frac{d}{dx}(x^{5}e^{3x})
integral of 9x^5e^{x^6}	\int\:9x^{5}e^{x^{6}}dx

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