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Popular Calculus Problems

integral of (3x^3+x)/(x^4+2x^2+1)	\int\:\frac{3x^{3}+x}{x^{4}+2x^{2}+1}dx
inverse oflaplace 1/((s^2+3)(s^2+1))	inverselaplace\:\frac{1}{(s^{2}+3)(s^{2}+1)}
integral of (sec^2(x))/(csc(x))	\int\:\frac{\sec^{2}(x)}{\csc(x)}dx
derivative of log_{10}(4x)	\frac{d}{dx}(\log_{10}(4x))
integral of 1/(t-1/2)	\int\:\frac{1}{t-\frac{1}{2}}dt
e^{-y}sin(x)+y^'=0	e^{-y}\sin(x)+y^{\prime\:}=0
derivative of 2xsqrt(x+1)	\frac{d}{dx}(2x\sqrt{x+1})
integral from-3 to 2 of (6-x-x^2)	\int\:_{-3}^{2}(6-x-x^{2})dx
derivative of e^{2sin^2(x})	\frac{d}{dx}(e^{2\sin^{2}(x)})
integral of (2/(x^3))	\int\:(\frac{2}{x^{3}})dx
tangent of f(x)=4x-4sqrt(x)	tangent\:f(x)=4x-4\sqrt{x}
(\partial)/(\partial x)(cos(-x))	\frac{\partial\:}{\partial\:x}(\cos(-x))
derivative of sqrt(14-x)	\frac{d}{dx}(\sqrt{14-x})
integral of 1/((x+3)sqrt(x^2+6x-7))	\int\:\frac{1}{(x+3)\sqrt{x^{2}+6x-7}}dx
integral of 0.0015x^2	\int\:0.0015x^{2}dx
(\partial)/(\partial x)((yx)/(y+x))	\frac{\partial\:}{\partial\:x}(\frac{yx}{y+x})
limit as x approaches 2 of x^2+3x+1	\lim\:_{x\to\:2}(x^{2}+3x+1)
limit as x approaches 0 of (ln(sin(2x)))/(ln(tan(x)))	\lim\:_{x\to\:0}(\frac{\ln(\sin(2x))}{\ln(\tan(x))})
integral of 1/(sqrt(9-81x^2))	\int\:\frac{1}{\sqrt{9-81x^{2}}}dx
derivative of (2x/(3-cot(x)))	\frac{d}{dx}(\frac{2x}{3-\cot(x)})
derivative of 5^{2x+6}(ln(5x+7))	derivative\:5^{2x+6}(\ln(5x+7))
integral of sqrt(9x^2-1)	\int\:\sqrt{9x^{2}-1}dx
derivative of f(x)=4sec(x)	derivative\:f(x)=4\sec(x)
derivative of (ln(6x))^{11}	derivative\:(\ln(6x))^{11}
limit as x approaches 5-of x/(x+1)	\lim\:_{x\to\:5-}(\frac{x}{x+1})
limit as x approaches 0 of sqrt(-x)	\lim\:_{x\to\:0}(\sqrt{-x})
integral of 6x^{1/2}	\int\:6x^{\frac{1}{2}}dx
derivative of (x+2)^8	derivative\:(x+2)^{8}
derivative of 2+sqrt(7x)	derivative\:2+\sqrt{7x}
derivative of cos(x-2tan(x))	\frac{d}{dx}(\cos(x)-2\tan(x))
inverse oflaplace 1/((x+1)^2)	inverselaplace\:\frac{1}{(x+1)^{2}}
limit as x approaches 5 of-5x^2	\lim\:_{x\to\:5}(-5x^{2})
integral of 4/(\sqrt[4]{x)}	\int\:\frac{4}{\sqrt[4]{x}}dx
sum from i=1 to infinity of (3/2)^i	\sum\:_{i=1}^{\infty\:}(\frac{3}{2})^{i}
derivative of x^2\sqrt[3]{x^2}	\frac{d}{dx}(x^{2}\sqrt[3]{x^{2}})
integral of (sqrt(x))/(x^2+x)	\int\:\frac{\sqrt{x}}{x^{2}+x}dx
derivative of x^2*e^{-x^2}	\frac{d}{dx}(x^{2}\cdot\:e^{-x^{2}})
tangent of f(x)=-x^2-2x-2,\at x=-3	tangent\:f(x)=-x^{2}-2x-2,\at\:x=-3
integral of (In(x))/(x^2)	\int\:\frac{In(x)}{x^{2}}dx
integral of (x^3)/(sqrt(x^2+5))	\int\:\frac{x^{3}}{\sqrt{x^{2}+5}}dx
integral of (2x+4)	\int\:(2x+4)dx
derivative of tan(pi/3)	\frac{d}{dx}(\tan(\frac{π}{3}))
integral of-(6x^3+8x)/(x^4-16)	\int\:-\frac{6x^{3}+8x}{x^{4}-16}dx
(dy}{dt}=0.1ln(\frac{4000)/y)y	\frac{dy}{dt}=0.1\ln(\frac{4000}{y})y
derivative of ln(7x)	derivative\:\ln(7x)
tangent of f(x)=log_{5}(2x^2+7),\at x=3	tangent\:f(x)=\log_{5}(2x^{2}+7),\at\:x=3
derivative of sin(x+2sin^2(x))	\frac{d}{dx}(\sin(x)+2\sin^{2}(x))
taylor 10^x,1	taylor\:10^{x},1
derivative of-8(64e^{-4x^2}x^3-24e^{-4x^2}x)	\frac{d}{dx}(-8(64e^{-4x^{2}}x^{3}-24e^{-4x^{2}}x))
derivative of y=11x^2e^x	derivative\:y=11x^{2}e^{x}
integral from 1 to 7 of 1/x	\int\:_{1}^{7}\frac{1}{x}dx
taylor x/(2-x)	taylor\:\frac{x}{2-x}
(\partial}{\partial x}(\frac{xy)/4)	\frac{\partial\:}{\partial\:x}(\frac{xy}{4})
integral of x^3-30x	\int\:x^{3}-30xdx
derivative of ((sqrt(2x+1)/(e+1))^e)	\frac{d}{dx}((\frac{\sqrt{2x+1}}{e+1})^{e})
(\partial)/(\partial x)(x\|x\|)	\frac{\partial\:}{\partial\:x}(x\left\|x\right\|)
limit as t approaches-1 of (e^t}{(\frac{e^t-6)/5)}	\lim\:_{t\to\:-1}(\frac{e^{t}}{(\frac{e^{t}-6}{5})})
integral from 0 to 5 of \|x-2\|	\int\:_{0}^{5}\left\|x-2\right\|dx
taylor (1+x)^5	taylor\:(1+x)^{5}
integral from 0 to 9 of 1/((x-1)^{1/3)}	\int\:_{0}^{9}\frac{1}{(x-1)^{\frac{1}{3}}}dx
tangent of f(x)=x^3-2x^2-5x+6,\at x=2	tangent\:f(x)=x^{3}-2x^{2}-5x+6,\at\:x=2
integral from 0 to 3 of 15sqrt(8x+1)	\int\:_{0}^{3}15\sqrt{8x+1}dx
integral of ge^{-ct}	\int\:ge^{-ct}dt
derivative of axsin(4x+bxcos(4x))	\frac{d}{dx}(ax\sin(4x)+bx\cos(4x))
f^'(t)-f(t)=2t	f^{\prime\:}(t)-f(t)=2t
integral of e^{2x+1}	\int\:e^{2x+1}dx
limit as x approaches 3+of (-x)/(x-3)	\lim\:_{x\to\:3+}(\frac{-x}{x-3})
limit as x approaches 8 of 3/((x-8)^2)	\lim\:_{x\to\:8}(\frac{3}{(x-8)^{2}})
integral of 13tan^4(x)sec^6(x)	\int\:13\tan^{4}(x)\sec^{6}(x)dx
tangent of (6x)/(x+5)	tangent\:\frac{6x}{x+5}
derivative of f(x)=2x^2-6x+4	derivative\:f(x)=2x^{2}-6x+4
integral of e^{(-s+4)t}t	\int\:e^{(-s+4)t}tdt
limit as x approaches 1 of (x^{-2}-6^{-2})/(x+6)	\lim\:_{x\to\:1}(\frac{x^{-2}-6^{-2}}{x+6})
integral of e^{(-3x)}	\int\:e^{(-3x)}dx
integral from 0 to 1 of (x^6+x^8)	\int\:_{0}^{1}(x^{6}+x^{8})dx
(dy)/(dx)+4xy=xe^{x^2}	\frac{dy}{dx}+4xy=xe^{x^{2}}
taylor x^2*e^x	taylor\:x^{2}\cdot\:e^{x}
limit as x approaches-5 of (3x+8)/(x+5)	\lim\:_{x\to\:-5}(\frac{3x+8}{x+5})
inverse oflaplace 4t	inverselaplace\:4t
limit as x approaches 14-of ln(14-x)	\lim\:_{x\to\:14-}(\ln(14-x))
tangent of y=e^{9x}cos(pix),(0,1)	tangent\:y=e^{9x}\cos(πx),(0,1)
derivative of ln(2-x)	derivative\:\ln(2-x)
tangent of 3x^3	tangent\:3x^{3}
y^'=xln(x)	y^{\prime\:}=x\ln(x)
derivative of (8x/5)	\frac{d}{dx}(\frac{8x}{5})
derivative of (3x^6+2x^3^4)	\frac{d}{dx}((3x^{6}+2x^{3})^{4})
integral of (2x+5)(x^2+5x)7	\int\:(2x+5)(x^{2}+5x)7dx
integral from 1 to n of xln(x)	\int\:_{1}^{n}x\ln(x)dx
(\partial)/(\partial x)((x^2+y)e^{y/2})	\frac{\partial\:}{\partial\:x}((x^{2}+y)e^{\frac{y}{2}})
integral of (4-x^2)^{3/2}	\int\:(4-x^{2})^{\frac{3}{2}}dx
((x+1)/(x-1))^'	(\frac{x+1}{x-1})^{\prime\:}
(dy)/(dt)=5y	\frac{dy}{dt}=5y
integral of x+x	\int\:x+xdx
derivative of y=(2x^5+8)/(x^3)	derivative\:y=\frac{2x^{5}+8}{x^{3}}
integral of 1/((2x^2-x-3))	\int\:\frac{1}{(2x^{2}-x-3)}dx
limit as x approaches infinity of (e^{2x})/(e^{2x)+1}	\lim\:_{x\to\:\infty\:}(\frac{e^{2x}}{e^{2x}+1})
integral of 1/(1+21x)	\int\:\frac{1}{1+21x}dx
derivative of f(x)=e^8	derivative\:f(x)=e^{8}
integral of cos(x)-sin(x)	\int\:\cos(x)-\sin(x)dx
area y=1-x^4,y=0	area\:y=1-x^{4},y=0

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