Q.1 (C) (iii) To find the value of ∫frac10x⁹+10^x·log 1010^x+x¹⁰ dx, the proper substitution is ____.

Answer: 10^x+x¹⁰=t d/dx(10^x+x¹⁰)=10^xlog 10+10x⁹, which is the numerator. So put 10^x+x¹⁰=t; then dt=(10x⁹+10^xlog 10)dx and the integral becomes ∫dt/t=log|10^x+x¹⁰|+c.

Chapter: Integration· Mathematics & Statistics (Commerce) Part 1

To find the value of \(\int\frac{10x^9+10^x\cdot\log 10}{10^x+x^{10}}\,dx\), the proper substitution is ____.

Q.1 (C) (iii) To find the value of \(\int\frac{10x^9+10^x\cdot\log 10}{10^x+x^{10}}\,dx\), the proper substitution is ____.

Doubtly Asked 29 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: \(10^x+x^{10}=t\)

\(\frac{d}{dx}\left(10^x+x^{10}\right)=10^x\log 10+10x^9\), which is the numerator. So put \(10^x+x^{10}=t\); then \(dt=(10x^9+10^x\log 10)dx\) and the integral becomes \(\int\frac{dt}{t}=\log|10^x+x^{10}|+c\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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To find the value of \(\int\frac{10x^9+10^x\cdot\log 10}{10^x+x^{10}}\,dx\), the proper substitution is ____.

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