9000150308 Level: AEvaluate the following integral on R. ∫cosx8dxsinx8+c, c∈R−sinx8+c, c∈Rsinx+c, c∈R−sinx+c, c∈R
1003027301 Level: BEvaluate the following indefinite integral on (0;π2). ∫(sinx+cosx)2−1sinxcosxdx2x+c, c∈Rx+c, c∈Rtgx+c, c∈Rc, c∈R
1003027302 Level: BEvaluate the following indefinite integral on (−π2;π2). ∫(1cosx−sinx⋅tgx)dxsinx+c, c∈Rcosx+c, c∈R−sinx+c, c∈R−cosx+c, c∈R
1003027303 Level: BChoose the function g whose derivative on (−π;0) is the following function: f(x)=sin2x⋅cotg2x+sin2x−1g(x)=5g(x)=x+3g(x)=tgxg(x)=sinx
1003027305 Level: BChoose an incorrect evaluation of the following indefinite integral on (0;∞). ∫(x−1)(x+1)dxx2−2x+c, c∈Rx22−x+c, c∈Rx2−2x2+c, c∈Rx4−4x22x(x+2)+c, c∈R
1003027306 Level: BEvaluate the following indefinite integral on (3;∞). ∫x2−5x+6x−3dxx22−2x+c, c∈Rx−2+c, c∈Rx22+2x+c, c∈Rx22−x+c, c∈R
1003107804 Level: BFour girls evaluated the integral I=∫sinx⋅cosxdx on R. Ann started to integrate by parts like this: I=∫sinx⋅cosxdx=sin2x−∫cosx⋅sinxdx. Beth started to integrate by parts like this: I=∫sinx⋅cosxdx=−cos2x−∫sinx⋅cosxdx. Claire used substitution a=sinx like this: I=∫sinx⋅cosxdx=∫ada. Diana integrated ∫sinx⋅cosxdx=−cosx⋅sinx+c, c∈R. Which of the girls made a mistake?DianaAnnBethClaire
1003107808 Level: BFind the indefinite integral ∫ln5xxdx on (0;∞). Use a substitution a=lnx.ln6x6+c, c∈R5ln4x+c, c∈Rln2x2+c, c∈R12ln5x+c, c∈R
1003107809 Level: BSolve an indefinite integral ∫8x7−30x5x8−5x6+2dx on (3;∞).ln|x8−5x6+2|+c, c∈Rln|8x7−30x5+2x|+c, c∈Rlog|x8−5x6+2|+c, c∈Rlog|8x7−30x5+2x|+c, c∈R
1103107802 Level: BWhat is the color of the graph of a function F(x), that is primitive to the function f(x)=2x+1 on (−1;∞)? (See the picture.)yellowgreenbluered