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Popular Calculus Problems

f(x)=sin(\sqrt[3]{x})*cos(\sqrt[3]{x})	f(x)=\sin(\sqrt[3]{x})\cdot\:\cos(\sqrt[3]{x})
integral from 4 to infinity of 8x^{-3}	\int\:_{4}^{\infty\:}8x^{-3}dx
tangent of f(x)= 2/(x-2),(4,1)	tangent\:f(x)=\frac{2}{x-2},(4,1)
tangent of f(x)= 4/x	tangent\:f(x)=\frac{4}{x}
integral of (x^2+2x)*cos(x)	\int\:(x^{2}+2x)\cdot\:\cos(x)dx
integral of \sqrt[3]{x}(x-3)	\int\:\sqrt[3]{x}(x-3)dx
integral of x^2e^{-x^2}	\int\:x^{2}e^{-x^{2}}dx
derivative of f(1/3 x^3)=2x^5	\frac{d}{dx}(f(\frac{1}{3}x^{3}))=2x^{5}
derivative of 2cos(x+(cos(x))^2)	\frac{d}{dx}(2\cos(x)+(\cos(x))^{2})
y^'=(y^4x^4+4x^4)/(y^3)	y^{\prime\:}=\frac{y^{4}x^{4}+4x^{4}}{y^{3}}
integral of (x+7)/(x^2(x+2))	\int\:\frac{x+7}{x^{2}(x+2)}dx
derivative of (cos(x2x^3)/(e^x))	\frac{d}{dx}(\frac{\cos(x)2x^{3}}{e^{x}})
limit as x approaches+1/5 of 2+\|5x-1\|	\lim\:_{x\to\:+\frac{1}{5}}(2+\left\|5x-1\right\|)
d/(dy)((y^3)/3+1/(4y))	\frac{d}{dy}(\frac{y^{3}}{3}+\frac{1}{4y})
integral from 0 to ln(20) of xe^x	\int\:_{0}^{\ln(20)}xe^{x}dx
(\partial)/(\partial x)(5x+4y)	\frac{\partial\:}{\partial\:x}(5x+4y)
integral of (x^2+3x-2)^2	\int\:(x^{2}+3x-2)^{2}dx
derivative of g(x)=y=2x,x=1	derivative\:g(x)=y=2x,x=1
(\partial)/(\partial y)(ln(1+y^2))	\frac{\partial\:}{\partial\:y}(\ln(1+y^{2}))
integral of sin(t/2)	\int\:\sin(\frac{t}{2})dt
integral of x^9e^{x^{10-9}}	\int\:x^{9}e^{x^{10-9}}dx
integral of 1/50 x	\int\:\frac{1}{50}xdx
(x+y)dx-xdy=0	(x+y)dx-xdy=0
integral from 0 to 1 of x^7	\int\:_{0}^{1}x^{7}dx
limit as x approaches-5-of 2/(x+5)	\lim\:_{x\to\:-5-}(\frac{2}{x+5})
tangent of f(x)=x^2+2,(4,18)	tangent\:f(x)=x^{2}+2,(4,18)
limit as x approaches-9+of (x+10)/(x+9)	\lim\:_{x\to\:-9+}(\frac{x+10}{x+9})
limit as x approaches-2+of-3x+5	\lim\:_{x\to\:-2+}(-3x+5)
limit as x approaches 5+of (\|x-5\|)/(x-5)	\lim\:_{x\to\:5+}(\frac{\left\|x-5\right\|}{x-5})
integral of 1/(2+7x^2)	\int\:\frac{1}{2+7x^{2}}dx
derivative of (1/2 ^x)	\frac{d}{dx}((\frac{1}{2})^{x})
y^{''}-9y^'+3y=xe^x	y^{\prime\:\prime\:}-9y^{\prime\:}+3y=xe^{x}
integral of (x^3+x^2+2x-3)	\int\:(x^{3}+x^{2}+2x-3)dx
derivative of (ax^2+bx+ce^{-x/6})	\frac{d}{dx}((ax^{2}+bx+c)e^{-\frac{x}{6}})
derivative of y=7sin(4x)	derivative\:y=7\sin(4x)
(\partial)/(\partial y)(x^2y^5)	\frac{\partial\:}{\partial\:y}(x^{2}y^{5})
limit as x approaches 1+of-2	\lim\:_{x\to\:1+}(-2)
y^'+2y=x^2y^3	y^{\prime\:}+2y=x^{2}y^{3}
f(x)=x^9e^x	f(x)=x^{9}e^{x}
derivative of inx^2	\frac{d}{dx}(inx^{2})
integral from 0 to pi/4 of 49sin^2(x)	\int\:_{0}^{\frac{π}{4}}49\sin^{2}(x)dx
integral of sec^7(x)	\int\:\sec^{7}(x)dx
(dy)/(dx)=cot(x+y+3)-1	\frac{dy}{dx}=\cot(x+y+3)-1
integral of (e^{2x}-1)/(e^{2x)+1}	\int\:\frac{e^{2x}-1}{e^{2x}+1}dx
limit as x approaches 6+of (8+x)/(6-x)	\lim\:_{x\to\:6+}(\frac{8+x}{6-x})
integral of x^3e^{(x^2)}	\int\:x^{3}e^{(x^{2})}dx
integral of (8x+3)	\int\:(8x+3)dx
(\partial)/(\partial y)(e^{xy}ln(y))	\frac{\partial\:}{\partial\:y}(e^{xy}\ln(y))
y^'=e^{-3x}	y^{\prime\:}=e^{-3x}
limit as x approaches 5 of (\|x-5\|)/(x-5)	\lim\:_{x\to\:5}(\frac{\left\|x-5\right\|}{x-5})
integral from 1 to 5 of x^2ln(x)	\int\:_{1}^{5}x^{2}\ln(x)dx
inverse oflaplace 1-1/(1+x)	inverselaplace\:1-\frac{1}{1+x}
derivative of 4x^2sqrt(5x+1)	\frac{d}{dx}(4x^{2}\sqrt{5x+1})
integral of 5/(4sin(x)+3cos(x))	\int\:\frac{5}{4\sin(x)+3\cos(x)}dx
x^2y^{''}+2xy^'-6y=0,y(1)=0,y^'(1)=-4	x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}-6y=0,y(1)=0,y^{\prime\:}(1)=-4
derivative of 2/(\sqrt[4]{x^3)}	derivative\:\frac{2}{\sqrt[4]{x^{3}}}
derivative of sin(ln(4x^2))	\frac{d}{dx}(\sin(\ln(4)x^{2}))
derivative of y=xsqrt(400-x^2)	derivative\:y=x\sqrt{400-x^{2}}
derivative of x^5sin(2x)	\frac{d}{dx}(x^{5}\sin(2x))
derivative of (x^2(x+1^2)/(sqrt(x-1)))	\frac{d}{dx}(\frac{x^{2}(x+1)^{2}}{\sqrt{x-1}})
derivative of 6sqrt(4x^2+5)	derivative\:6\sqrt{4x^{2}+5}
derivative of e^{y-ln(x})	\frac{d}{dx}(e^{y-\ln(x)})
derivative of (x^4/(sqrt(x^5+3)))	\frac{d}{dx}(\frac{x^{4}}{\sqrt{x^{5}+3}})
(\partial)/(\partial y)(3x+y)	\frac{\partial\:}{\partial\:y}(3x+y)
integral of (23)/(23+e^x)	\int\:\frac{23}{23+e^{x}}dx
(\partial)/(\partial x)(xy+ln(x+y))	\frac{\partial\:}{\partial\:x}(xy+\ln(x+y))
derivative of sin^{ln(x}(3x))	\frac{d}{dx}(\sin^{\ln(x)}(3x))
integral of sin(sqrt(at))	\int\:\sin(\sqrt{at})dt
derivative of e^{3x}+10e^{2x}	\frac{d}{dx}(e^{3x}+10e^{2x})
t^2y^'+3ty+2t^3=0	t^{2}y^{\prime\:}+3ty+2t^{3}=0
(e^y+6x)dx+(xe^y)dy=0	(e^{y}+6x)dx+(xe^{y})dy=0
integral of e^{ln(2t)}	\int\:e^{\ln(2t)}dt
inverse oflaplace 1/((s+1)^2(s+2))	inverselaplace\:\frac{1}{(s+1)^{2}(s+2)}
tangent of-5/2 x^2+2x+2	tangent\:-\frac{5}{2}x^{2}+2x+2
integral of 3x^2y^2	\int\:3x^{2}y^{2}dx
integral from 3 to 5 of (x^4-3/(x^3))	\int\:_{3}^{5}(x^{4}-\frac{3}{x^{3}})dx
2(ln(y))y^'-x^5y=0	2(\ln(y))y^{\prime\:}-x^{5}y=0
derivative of y=cos(a^5+x^5)	derivative\:y=\cos(a^{5}+x^{5})
integral from 2 to 4 of 3/x	\int\:_{2}^{4}\frac{3}{x}dx
(\partial)/(\partial x)(2ysin(x)+e^{2z})	\frac{\partial\:}{\partial\:x}(2y\sin(x)+e^{2z})
limit as x approaches 0-of e^{-7/x}	\lim\:_{x\to\:0-}(e^{-\frac{7}{x}})
integral of-1/(2xsqrt(x^2+9))	\int\:-\frac{1}{2x\sqrt{x^{2}+9}}dx
derivative of e^{x^5}+log_{4}(pi)	derivative\:e^{x^{5}}+\log_{4}(π)
limit as n approaches infinity of a/n	\lim\:_{n\to\:\infty\:}(\frac{a}{n})
limit as x approaches 5-of (\|x-5\|)/(x-5)	\lim\:_{x\to\:5-}(\frac{\left\|x-5\right\|}{x-5})
derivative of (x^2/(7x+4))	\frac{d}{dx}(\frac{x^{2}}{7x+4})
(\partial)/(\partial y)(x^2*y)	\frac{\partial\:}{\partial\:y}(x^{2}\cdot\:y)
derivative of (4x/(6x-1))	\frac{d}{dx}(\frac{4x}{6x-1})
limit as x approaches 4 of sqrt(2x-7)	\lim\:_{x\to\:4}(\sqrt{2x-7})
integral of bx^2	\int\:bx^{2}dx
(2/((1+x)^3))^'	(\frac{2}{(1+x)^{3}})^{\prime\:}
integral of 1+2x^2	\int\:1+2x^{2}dx
integral from-3 to 2 of pi(y^2+2y+4)^2	\int\:_{-3}^{2}π(y^{2}+2y+4)^{2}dy
(dy)/(dx)= 1/(sqrt(1-x))	\frac{dy}{dx}=\frac{1}{\sqrt{1-x}}
integral of tcsc^2(t)	\int\:t\csc^{2}(t)dt
integral of 6xe^{-x}	\int\:6xe^{-x}dx
integral of 1/(sin(x)cos^5(x))	\int\:\frac{1}{\sin(x)\cos^{5}(x)}dx
derivative of x(x-7^2)	\frac{d}{dx}(x(x-7)^{2})
derivative of 7/(4-3x)	\frac{d}{dx}(\frac{7}{4-3x})
derivative of f(x)=(x+x^3)/(sqrt(x))	derivative\:f(x)=\frac{x+x^{3}}{\sqrt{x}}

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