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Popular Calculus Problems

integral from 1 to e^7 of (ln^2(x^2))/x	\int\:_{1}^{e^{7}}\frac{\ln^{2}(x^{2})}{x}dx
sum from n=1 to infinity of (3/n)^4	\sum\:_{n=1}^{\infty\:}(\frac{3}{n})^{4}
integral of 1/(sin^2(t))	\int\:\frac{1}{\sin^{2}(t)}dt
derivative of r=10^{2sqrt(t)}	derivative\:r=10^{2\sqrt{t}}
(\partial)/(\partial x)(sin(pi(4x-3y)))	\frac{\partial\:}{\partial\:x}(\sin(π(4x-3y)))
sum from n=1 to infinity}((\sqrt{n of))/(ln(n))	\sum\:_{n=1}^{\infty\:}\frac{(\sqrt{n})}{\ln(n)}
(\partial)/(\partial x)(x+y+ln(xy))	\frac{\partial\:}{\partial\:x}(x+y+\ln(xy))
integral of sqrt(1-\sqrt{v)}	\int\:\sqrt{1-\sqrt{v}}dv
integral of cot(1)	\int\:\cot(1)dx
(\partial)/(\partial x)(log_{e}(x^2+y^4))	\frac{\partial\:}{\partial\:x}(\log_{e}(x^{2}+y^{4}))
integral of sin(8pix)	\int\:\sin(8πx)dx
integral of 1/(2x^{1/2)}	\int\:\frac{1}{2x^{\frac{1}{2}}}dx
tangent of 4x^3-12x^2	tangent\:4x^{3}-12x^{2}
(\partial)/(\partial x)(x^4y^4+8x^9y)	\frac{\partial\:}{\partial\:x}(x^{4}y^{4}+8x^{9}y)
integral of x-1/x	\int\:x-\frac{1}{x}dx
tangent of y=(e^{-x})/(x+1)	tangent\:y=\frac{e^{-x}}{x+1}
integral of 1/(x^2+3x+1)	\int\:\frac{1}{x^{2}+3x+1}dx
slope of-2x^5+10x^3	slope\:-2x^{5}+10x^{3}
integral of (e^x)/(e^{2x)+4e^x+4}	\int\:\frac{e^{x}}{e^{2x}+4e^{x}+4}dx
derivative of cos((1-e^{2x})/(1+e^{2x)})	derivative\:\cos(\frac{1-e^{2x}}{1+e^{2x}})
integral from 6 to 7 of (tsqrt(t-6))	\int\:_{6}^{7}(t\sqrt{t-6})dt
derivative of 3x^2+2y^2	\frac{d}{dx}(3x^{2}+2y^{2})
y^'=3(y+1)	y^{\prime\:}=3(y+1)
derivative of (cos(x))/(sin(x))	derivative\:\frac{\cos(x)}{\sin(x)}
area y=10x^3,y=10x^2	area\:y=10x^{3},y=10x^{2}
integral of 1/(2sqrt(x^3))	\int\:\frac{1}{2\sqrt{x^{3}}}dx
x(dy)/(dx)=2	x\frac{dy}{dx}=2
derivative of (91t)/(99t-91)	derivative\:\frac{91t}{99t-91}
derivative of 2xe^{2x}+e^{2x}	\frac{d}{dx}(2xe^{2x}+e^{2x})
limit as x approaches 0 of ((x+3))/x	\lim\:_{x\to\:0}(\frac{(x+3)}{x})
integral of sqrt(1+e^{-2x)}	\int\:\sqrt{1+e^{-2x}}dx
derivative of a(sin(x+xcos(x)))	\frac{d}{dx}(a(\sin(x)+x\cos(x)))
integral of 3cos^5(3x)	\int\:3\cos^{5}(3x)dx
integral of (e^{2x})/(e^x+4)	\int\:\frac{e^{2x}}{e^{x}+4}dx
derivative of ln^3(5x)	\frac{d}{dx}(\ln^{3}(5x))
(\partial)/(\partial y)(2xyz^{-1})	\frac{\partial\:}{\partial\:y}(2xyz^{-1})
y^'=e^{5y+8x}	y^{\prime\:}=e^{5y+8x}
integral of 1/(e^{3x)}	\int\:\frac{1}{e^{3x}}dx
ydx-xdy+xydy=0	ydx-xdy+xydy=0
sum from n=0 to infinity of 2/(n(n+2))	\sum\:_{n=0}^{\infty\:}\frac{2}{n(n+2)}
(\partial)/(\partial x)(e^{(xy)^{1/2}})	\frac{\partial\:}{\partial\:x}(e^{(xy)^{\frac{1}{2}}})
integral of yln(x)	\int\:y\ln(x)dx
limit as x approaches 9 of 6x+\|x-9\|	\lim\:_{x\to\:9}(6x+\left\|x-9\right\|)
(dx)/(dy)=5(40-x)	\frac{dx}{dy}=5(40-x)
derivative of (x^2/(x^2+16))	\frac{d}{dx}(\frac{x^{2}}{x^{2}+16})
y^{''}-y=x^2-3x	y^{\prime\:\prime\:}-y=x^{2}-3x
derivative of f(x)= 1/(4x)	derivative\:f(x)=\frac{1}{4x}
derivative of x^3e^{3x}	\frac{d}{dx}(x^{3}e^{3x})
maclaurin 20e^{-x}	maclaurin\:20e^{-x}
integral of ((ln(x))/(x^3))	\int\:(\frac{\ln(x)}{x^{3}})dx
integral from 0 to 1 of x/(e^x)	\int\:_{0}^{1}\frac{x}{e^{x}}dx
(dx)/(dt)=x^2+1/49	\frac{dx}{dt}=x^{2}+\frac{1}{49}
(\partial)/(\partial x)(ln(xy)+xe^y)	\frac{\partial\:}{\partial\:x}(\ln(xy)+xe^{y})
integral of (2x)/(sqrt(u))	\int\:\frac{2x}{\sqrt{u}}
limit as t approaches 1 of t^{1/(t-1)}	\lim\:_{t\to\:1}(t^{\frac{1}{t-1}})
integral of (4sin(x)+5cos(x))	\int\:(4\sin(x)+5\cos(x))dx
integral of (3x^2+4x^3)/(x^3+x^4)	\int\:\frac{3x^{2}+4x^{3}}{x^{3}+x^{4}}dx
integral of 2/(10+x)	\int\:\frac{2}{10+x}dx
derivative of f(x)= 2/(3x+5)	derivative\:f(x)=\frac{2}{3x+5}
area y=3sqrt(x),y=(3x)/2	area\:y=3\sqrt{x},y=\frac{3x}{2}
derivative of-tan^2(x)	\frac{d}{dx}(-\tan^{2}(x))
inverse oflaplace 4x-3	inverselaplace\:4x-3
(\partial)/(\partial x)(9e^{x-y})	\frac{\partial\:}{\partial\:x}(9e^{x-y})
sum from n=2 to infinity of 4/(7^n)	\sum\:_{n=2}^{\infty\:}\frac{4}{7^{n}}
derivative of f(x)=a^5+cos^5(x)	derivative\:f(x)=a^{5}+\cos^{5}(x)
tangent of f(x)=x^2-3x,\at x=2	tangent\:f(x)=x^{2}-3x,\at\:x=2
tangent of y=(6x)/(x^2+1),(1,1)	tangent\:y=\frac{6x}{x^{2}+1},(1,1)
derivative of x^3-2x+7	\frac{d}{dx}(x^{3}-2x+7)
derivative of cos(ln(x)-sin(ln(x)))	\frac{d}{dx}(\cos(\ln(x))-\sin(\ln(x)))
d/(dy)(2y^3+1/(24y))	\frac{d}{dy}(2y^{3}+\frac{1}{24y})
derivative of 3x^2+5x	\frac{d}{dx}(3x^{2}+5x)
limit as x approaches 1+of x^{6/(1-x)}	\lim\:_{x\to\:1+}(x^{\frac{6}{1-x}})
derivative of ((x-3(x^2+3x+9))/(x^3))	\frac{d}{dx}(\frac{(x-3)(x^{2}+3x+9)}{x^{3}})
d/(dy)(3/y)	\frac{d}{dy}(\frac{3}{y})
integral of 1/(xln(x^2))	\int\:\frac{1}{x\ln(x^{2})}dx
derivative of 2x^3+x^2	\frac{d}{dx}(2x^{3}+x^{2})
y^'=-y^2	y^{\prime\:}=-y^{2}
d/(dt)(Ate^{-4t})	\frac{d}{dt}(Ate^{-4t})
integral from 2 to 3 of (12)/(sqrt(3-x))	\int\:_{2}^{3}\frac{12}{\sqrt{3-x}}dx
integral from 0 to 1 of 7/(1+x^2)	\int\:_{0}^{1}\frac{7}{1+x^{2}}dx
inverse oflaplace (10s-3)/(s^2+4s+29)	inverselaplace\:\frac{10s-3}{s^{2}+4s+29}
derivative of 1/(3-x)	derivative\:\frac{1}{3-x}
integral from 1 to e of (x^2+x+1)/x	\int\:_{1}^{e}\frac{x^{2}+x+1}{x}dx
integral from-2 to 3 of (19)/(x^4)	\int\:_{-2}^{3}\frac{19}{x^{4}}dx
limit as x approaches 2 of-1/(x-2)	\lim\:_{x\to\:2}(-\frac{1}{x-2})
integral of (3-x^2)^3	\int\:(3-x^{2})^{3}dx
derivative of f(x)=e^{x^3}	derivative\:f(x)=e^{x^{3}}
limit as x approaches-5+of (-2)/(x^2-25)	\lim\:_{x\to\:-5+}(\frac{-2}{x^{2}-25})
d/(dt)(1/(1+t^2))	\frac{d}{dt}(\frac{1}{1+t^{2}})
(dy)/(dx)= x/y ,y(0)=-2	\frac{dy}{dx}=\frac{x}{y},y(0)=-2
inverse oflaplace 6/s+(24)/(s^2+16)	inverselaplace\:\frac{6}{s}+\frac{24}{s^{2}+16}
limit as x approaches 6 of 3/x	\lim\:_{x\to\:6}(\frac{3}{x})
derivative of (e^x/(e^x+2))	\frac{d}{dx}(\frac{e^{x}}{e^{x}+2})
integral of xsec^2(2x)	\int\:x\sec^{2}(2x)dx
maclaurin ln(1/(1-x))	maclaurin\:\ln(\frac{1}{1-x})
(x^2y^3-1/(1+9x^2))dx+(x^3y^2)dy=0	(x^{2}y^{3}-\frac{1}{1+9x^{2}})dx+(x^{3}y^{2})dy=0
derivative of sin^2(x-cos^2(x))	\frac{d}{dx}(\sin^{2}(x)-\cos^{2}(x))
limit as x approaches 5 of 3/(x-5)	\lim\:_{x\to\:5}(\frac{3}{x-5})
derivative of \|x\|^x	\frac{d}{dx}(\left\|x\right\|^{x})
integral of 1/(x-sqrt(x-2))	\int\:\frac{1}{x-\sqrt{x-2}}dx

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