What is the correct antiderivative of ∫ sin^3(10x) dx?
∫ sin^3(10x) dx का सही antiderivative क्या है?
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Correct Answer
C. -cos(10x) / 10 + cos^3(10x) / 30 + C
ExplanationStep 1: write sin^3(10x) as sin(10x)(1-cos²(10x)). Step 2: using u=cos(10x), adjust the factor 10 and get -cos(10x)/10 + cos^3(10x)/30 + C. Step 3: tip: for odd sine powers, keep one sine factor for substitution.
Step 1: sin^3(10x) को sin(10x)(1-cos²(10x)) लिखें। Step 2: u=cos(10x) लेने पर factor 10 adjust होता है और answer -cos(10x)/10 + cos^3(10x)/30 + C मिलता है। Step 3: tip: odd sine power में one sine factor substitution के लिए रखें।